The number of points on the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` from which mutually perpendicular tangents can be drawn to the circle `x^2+y^2=a^2` is/are (a) 0 (b) 2 (c) 3 (d) 4

The number of points on the ellipse (x^2)/(50)+(y^2)/(20)=1 from which a pair of perpendicular tangents is drawn to the ellipse (x^2)/(16)+(y^2)/9=1 is 0 (b) 2 (c) 1 (d) 4

Number of points from where perpendicular tangents can be drawn to the curve x^2/16-y^2/25=1 is

If there exists at least one point on the circle x^(2)+y^(2)=a^(2) from which two perpendicular tangents can be drawn to parabola y^(2)=2x , then find the values of a.

If eight distinct points can be found on the curve |x|+|y|=1 such that from eachpoint two mutually perpendicular tangents can be drawn to the circle x^2+y^2=a^2, then find the range of adot

If tangents drawn from the point (a ,2) to the hyperbola (x^2)/(16)-(y^2)/9=1 are perpendicular, then the value of a^2 is _____

From any point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=2. The area cut-off by the chord of contact on the asymptotes is equal to: (a) a/2 (b) a b (c) 2a b (d) 4a b

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola. (a) Statement 1 and Statement 2 are correct and Statement 2 is the correct explanation for Statement 1. (b) Statement 1 and Statement 2 are correct and Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

For hyperbola x^2/a^2-y^2/b^2=1 , let n be the number of points on the plane through which perpendicular tangents are drawn.

Mutually perpendicular tangents T A and T B are drawn to y^2=4a x . Then find the minimum length of A B