Bissoy.com
Doctors Medicines MCQs Q&A

If the distances of P (x, y) from A (4, 1) and B (-1, 4) are equal, then which of the following is true?

If the distances of P (x, y) from A (4, 1) and B (-1, 4) are equal, then which of the following is true? Correct Answer 5x = 3y

Concept:

The distance 'd' between two points (x1, y1) and (x2, y2) is obtained by using the Pythagoras' Theorem: d2 = (x1 - x2)2 + (y1 - y2)2.

 

Calculation:

Using the formula for the distance between two points:

AP2 = (x - 4)2 + (y - 1)2

BP2 = (x + 1)2 + (y - 4)2

Since the distances are equal, we have:

AP2 = BP2

⇒ (x - 4)2 + (y - 1)2 = (x + 1)2 + (y - 4)2

⇒ x2 - 8x + 16 + y2 - 2y + 1 = x2 + 2x + 1 + y2 - 8y + 16

⇒ 10x = 6y

⇒ 5x = 3y.

Related Questions

Which of the following statements are true relating to payment of equal pay for equal work both for men and women?
1. ILO adopted equal remuneration Convention No. 100 in 1951.
2. India ratified ILO's Equal Remuneration Convention No. 100 in the year 1956.
3. Provisions relating to equal pay for equal work for both men and women are provided under Article 42 of the Indian Constitution.
4. The Equal Remuneration Ordinance was promulgated on 26th September, 1975.
From an alloy, two specimens are machined and tested separately under tension and compression. The engineering stress-strain curves as well as the true stress-true strain curves for tension and compression are plotted in the same diagram. Identify the correct statements:
P. The engineering stress-strain curves in tension and compression are identical.
Q. The true stress-true strain curve in compression is lower than the true stresstrue strain curve in tension due to Bauschinger effect.
R. The true stress-true strain curve in tension is above the corresponding engineering stress-strain, curve.
S. The true stress-true strain curve in tension and compression are identical.
Read the passage carefully and select the best answer to each question out of the given four alternatives.
Public opinion may be passive and false or active and real. It is claimed in theory that all governments are ultimately based on the opinion or sanction of the governed. But we find that in practice the people's rights are often trodden down and tyranny and oppression are allowed to continue. The government does it not because the people want it to do so but because they are too idle, too uneducated and too disunited or timid to oppose the govern ment. Such public opinion is passive and false and not an active verdict. But when we find people alert, intelligent and determined to let the government know their will, when they want to exercise actively their voice in the management of their country, we have an instance of true or active public opinion. True public opinion is formed by and expressed through the press, the platform, political parties and educational institutions. These have sacred duties to perform, duties on which depends the ultimate good of the entire community. The press today wields a tremendous influence, So it should support the causes and move ments and condemn the wrong one's and thus teach people to form correct opinion. A free and fair press ventilates the grievances of the public. Thus a healthy relationship develops between the people and the government through out an unbiased press. Political parties also help to create and regulate opinions. No less important part is played by the educational Institutions which train the minds of the young people who will be the citizens of tomorrow. It has been said that modern Germany and China have been made by their universities. It is necessary that the young and the growing minds should imbibe the spirit of fellow-feeling, the spirit of tolerance, the habit of compromise, and show due regard for the feelings and opinion of others without which a democratic society cannot function, let alone succeed. When there is true awakening of the people, we shall have the real and conscious public opinion. And justice will reign on earth and truly will the voice of the people be the voice of God.
According to the passage, which of the following is needed from the people to have true or active public opinion? 1. Alertness
2. Determination
3. Intelligence
4. Raising their voice
Read the passage carefully and select the best answer to each question out of the given four alternatives.
Public opinion may be passive and false or active and real. It is claimed in theory that all governments are ultimately based on the opinion or sanction of the governed. But we find that in practice the people's rights are often trodden down and tyranny and oppression are allowed to continue. The government does it not because the people want it to do so but because they are too idle, too uneducated and too disunited or timid to oppose the govern ment. Such public opinion is passive and false and not an active verdict. But when we find people alert, intelligent and determined to let the government know their will, when they want to exercise actively their voice in the management of their country, we have an instance of true or active public opinion. True public opinion is formed by and expressed through the press, the platform, political parties and educational institutions. These have sacred duties to perform, duties on which depends the ultimate good of the entire community. The press today wields a tremendous influence, So it should support the causes and move ments and condemn the wrong one's and thus teach people to form correct opinion. A free and fair press ventilates the grievances of the public. Thus a healthy relationship develops between the people and the government through out an unbiased press. Political parties also help to create and regulate opinions. No less important part is played by the educational Institutions which train the minds of the young people who will be the citizens of tomorrow. It has been said that modern Germany and China have been made by their universities. It is necessary that the young and the growing minds should imbibe the spirit of fellow-feeling, the spirit of tolerance, the habit of compromise, and show due regard for the feelings and opinion of others without which a democratic society cannot function, let alone succeed. When there is true awakening of the people, we shall have the real and conscious public opinion. And justice will reign on earth and truly will the voice of the people be the voice of God.
Who among the following has tremendous influence in forming the true public opinion?
Two processes X and Y need to access a critical section. Consider the following synchronization construct used by both the processes Process ? /* other code for process ? */ while(true) { varP = true; while(varQ == true) { /* Critical Section */ varP = false; } } /* other code for process ?? */   Process ? /* other code for process ? */ while(true) { varQ = true; while(varP == true) { /* Critical Section */ varQ = false; } } /* other code for process ? */   Here, varP and varQ are shared variables and both are initialized to false. Which one of the following statements is true?
A man divided his journey into three parts of distances of 18 km, 20 km and 27 km. He travelled the distances at the speeds of 6 km/h, 5 km/h and 9 km/h, respectively. What was his average speed during the entire journey?
A man divided his journey into three parts of distances of 36 km, 40 km and 54 km. He travelled the distances at the speeds of 12 km/h, 10 km/h and 9 km/h respectively. What was his average speed during the entire journey?
A man divided his journey into three parts of distances of 18 km, 20 km, and 27 km. He travelled the distances at the speeds of 6 km/h, 5 km/h, and 9 km/h, respectively. What was his average speed during the entire journey?
In Jukes–Cantor Model to correct evolutionary distances, A formula for deriving evolutionary distances that include hidden changes is introduced by using a logarithmic function. It is ____ b) dAB = −(3/4) ln c) dAB = −(3/4) log d) dAB = −(3/4) ln
P, Q, R, S, T, W, Y and Z are sitting around a circular table from equal distances to each other and facing towards centre. They all like different colours viz., Red, Blue, Green, Black, White, Pink, Yellow and Brown (not necessarily in the same order). P likes yellow and sitting third to the left of W. Two persons are sitting between W and S. The one who likes pink is not sitting with P nor with W. Only one person is sitting between T and Z but not P and S. Y likes black but he is not sitting with S. R does not like pink nor white. T is sitting to the immediate left one who likes green. Z does not like brown nor he is sitting to the immediate right one who likes black. The one who likes white is not sitting with W. R neither likes brown nor Red. Which of the following combination is true as per the given information?