JEE Advanced2018MathematicsCircleActual
Paragraph: Let S be the circle in the x y – plane defined by the equation x 2 + y 2 = 4 . Question : Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and M N Then, the mid-point of the line segment must lie on the curve
Options
- Ax + y 2 = 3 x y
- Bx 2 3 + y 2 3 = 2 4 3
- Cx 2 + y 2 = 2 x y
- Dx 2 + y 2 = x 2 y 2
Correct answer
D. x 2 + y 2 = x 2 y 2
Step-by-step solution
Tangent at P 2 cos ⁡ θ , 2 sin ⁡ θ i s   x cos ⁡ θ + y sin ⁡ θ = 2 M 2 sec ⁡ θ , 0   a n d   N 0,2 cosce ⁡ θ Let midpoint be (h, k) h = sec ⁡ θ , k = cosce ⁡ θ 1 h 2 + 1 k 2 = 1 1 x 2 + 1 y 2 = 1