Bissoy.com
Doctors Medicines MCQs Q&A

If circles x2 + y2 + 8x - 14y + p = 0 and x2 + y2 + 12x + 6y + q = 0 are orthogonal to each other, then what will be the value of 5p + 5q?

If circles x2 + y2 + 8x - 14y + p = 0 and x2 + y2 + 12x + 6y + q = 0 are orthogonal to each other, then what will be the value of 5p + 5q? Correct Answer 30

Calculation:

Condition of orthogonality = 2g1g2 + 2f1f2 = c1 + c2

Calculations:

Given: circles are x2 + y2 + 8x - 14y + p = 0 and x2 + y2 + 12x + 6y + q = 0

So g1 = 4, g2 = 6, f1 = - 7, f2 = 3, c1 = p, c2 = q

2g1g2 + 2f1f2 = c1 + c2 = 2. (4). (6) + 2. ( - 7). (3) = 6

So c1 + c2 = p + q = 6

So 5p + 5q = 5(p + q) = 5×6 = 30

Related Questions

Let x̅1 and x̅2 (where x̅2 > x̅1) be the means of two sets comprising n1 and n2 (where n2 < n1) observations respectively. If x̅ is the mean when they are pooled, then which one of the following is correct?
If x = 11, then the value of x5 - 12x4 + 12x3 - 12x2 + 12x - 1 is?
If x - 11, then the value of x5 - 12x4 + 12x3 - 12x2 + 12x - 1 is?
Four equal circles are drawn on the four sides of a square in such a way that each of the circles touches two other circles. What will be the area outside the perimeter of the circles towards the middle of the square? If the measure of each side of the square is 28 cm. 
In the following question, some statements are given followed by four conclusions. You have to take the given statements to be true even if they varies from commonly known facts. Read all the conclusions and decide which of the given conclusions logically follows from the commonly known facts. Statements: All squares are circles. Some rectangles are circles. Some triangles are rectangles. All triangles are hexagons. Conclusions: I. Some triangles are circles. II. Some rectangles are hexagons. III. Some triangles are both rectangles and circles. IV. Some squares are hexagons.
12x-1 +12x-1 2+12x-1 3 + . . . . .  ধারাটির অসীমতক সমষ্টি কতা
12x+1+12x+12+12x+13 + . . . . .  একটি অসীম গুণোত্তর ধারা। x এর উপর কী শর্ত আরোপ করলে ধারাটির অসীমতক সমষ্টি থাকবে?
There is a square with four circles drawn such that the four corners of the square are the centers of the four circles. What is the ratio of the area of the square to the area enclosed between the circumferences of the circles? The radius of the circle is given as 7 units and the side of the square is equal to the diameter of the circles.
There is a square with four circles drawn such that the four corners of the square are the centers of the four circles. What is the ratio of the area of the square to the area enclosed between the circumferences of the circles? The radius of the circle is given as 7 units and side of the square is equal to the diameter of the circles.
Two circles of same radius intersect each other at P and Q. If the length of the common chord is 30 cm and distance between the centres of the two circles is 40 cm, then what is the radius (in cm) of the circles?