InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If the tangent from a point p to the circle `x^2+y^2=1` is perpendicular to the tangent from p to the circle `x^2 +y^2 = 3` , then the locus of p isA. a circle of radius 2B. a circle of radius 4C. a circle of radius 3D. none of these |
|
Answer» Correct Answer - A The equation of tangent to `x^(2)+y^(2)=1` is ` x cos alpha + y sin alpha = 1 " " ...(i)` The equation of the tangent to `x^(2)+y^(2)=3`, perpendicular to (i), is `x sin alpha - y sin alpha = sqrt(3) " " (ii)` Let the coordinates of P be (h, k). Then, `h cos alpha + k sin alpha = 1 ` and `h sin alpha - k cos alpha = sqrt(3)` Eliminating (h, k) from these two equations, we get `h^(2) + k^(2)=4` Hence, the locus of (h, k) is `x^(2)+y^(2)-4`, which is a circle of radius 2. |
|