Bissoy.com
Doctors Medicines MCQs Q&A

The locus of the point of intersection of the lines x cos α + y sin α = a and x sin α - y cos α = b is

The locus of the point of intersection of the lines x cos α + y sin α = a and x sin α - y cos α = b is Correct Answer A circle

Concept:

The general equation of a non-degenerate conic section is: ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 where a, h and b are all not zero

The above-given equation represents a non-degenerate conics whose nature is given below in the table:

S.No

Condition

Nature of Conic

1

h = 0 and a = b

Circle

2

h = 0 and Either a = 0 or b = 0

Parabola

3

h = 0, a ≠ b and ab > 0

Ellipse

4

h = 0, a ≠ b and sign of a and b are opposite

Hyperbola

 

Calculation:

(i) 

(ii)

Squaring both sides of (i) and (ii) and adding both the equation we get  x2 + y2 = a2 + b2.

By comparing the given equation with ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, we get

⇒ a = 1, h = 0, b = 1

Here, we can see that h = 0, a = b

Which represents the locus of the circle.

Related Questions

Evaluate the following:
$$\frac{{\cos 2\theta \cdot \cos 3\theta - \cos 2\theta \cdot \cos 7\theta + \cos \theta \cdot \cos 10\theta }}{{\sin 4\theta \cdot \sin 3\theta - \sin 2\theta \cdot \sin 5\theta + \sin 4\theta \cdot \sin 7\theta }}$$
How far is point 'R' from Point 'T'? Statement (I): Point 'R' is 5 metres to the north of point 'M'. Point 'U' is 4 metres to the east of point 'R'. Point 'T' is to the west of point 'R' such that points 'U' 'R' and 'T' form a straight line of  metres. Statement (II): Point 'Z' is metres to the south of point 'T'. Point 'U' is  metres to the east of point 'T'. Point 'M' is  metres to the east of point 'Z'. Point 'R' is  metres to the north of point 'M'. Point 'R' lies on the line formed by joining points 'T' and 'U'.
Find the ∫∫x3 y3 sin⁡(x)sin⁡(y) dxdy. ]) b) (-x3 Cos(x) – 3x2 Sin(x) – 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3]) c) (-x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3y2 Sin(y) + 6yCos(y) – 6Sin(y)) d) (–x3 Cos(x) + 6xCos(x) – 6Sin(x))(-y3 Cos(y))
Point A is 3m in the north of point B. Point D is 2m in the east of point E. Point F is 9m in the west of point G. Point C is 4m in the west of point B. Point C is 3m in the south of point D. Point F is 5m in the south of point E. Point H is 5m in the north of point G. What is the shortest distance between point H and point A?
The value of the expression:sin21° + sin211° + sin221° + sin231° + sin241° + sin245° + sin249° + sin259° + sin269° + sin279° + sin289° is?
Point P is 4m in the west of point V. Point R is 6m in the north of point Q. Point T is 5m in the south of point S. Point V is in the middle of point R and Q. Point U is 5m in the east of point R. Point V is in north of point Q. Point S is 5m in the east of point V. What is the area of triangle formed by point P, R and Q?
What is the value of {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]?
Garima starts walking towards the south from point R. He walks for 5m to reach Point S then turns right and walks for 2m to reach point T from there he turns left and walks for 3m to reach Point Z. He then turns right from point Z and walks for 6m to reach point Y and then turns right and walks for 3m to reach point X. He then turns right from point X and walks for 4m to reach point W and then turns left and walks for 5m to reach point V and then turns left and walks for 4m till point U and stops. What is the shortest distance between point V and point R?
Study the following information and answer the questions. Point A is 8m to the west of Point B. Point C is 4m to the south of Point B. Point D is 4m to the east of Point C. Point F is 6m to the north of Point D. Point E is 8m to the west of Point F. Point G is 2m to the south of Point E. How far and in which direction is Point G from Point A?
Study the following information and answer the questions. Point A is 8m to the west of Point B. Point C is 4m to the south of Point B. Point D is 4m to the east of Point C. Point F is 6m to the north of Point D. Point E is 8m to the west of Point F. Point G is 2m to the south of Point E. If point G is 4m to the north of Point H, then what is the distance between H and D?