Radius of the circle that passes through the origin and touches the parabola `y^2=4a x` at the point `(a ,2a)` is (a)`5/(sqrt(2))a` (b) `2sqrt(2)a` (c)`sqrt(5/2)a` (d) `3/(sqrt(2))a`

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

If a line passing through the origin touches the circle (x-4)^2+(y+5)^2=25 , then find its slope.

The radius of the circle passing through the foci of the ellipse (x^2)/(16)+(y^2)/9 and having its center (0, 3) is (a)4 (b) 3 (c) sqrt(12) (d) 7/2

If (alpha,beta) is a point on the circle whose center is on the x-axis and which touches the line x+y=0 at (2,-2), then the greatest value of alpha is (a) 4-sqrt(2) (b) 6 (c) 4+2sqrt(2) (d) +sqrt(2)

The radius of the circle touching the parabola y^2=x at (1, 1) and having the directrix of y^2=x as its normal is (a)(5sqrt(5))/8 (b) (10sqrt(5))/3 (c)(5sqrt(5))/4 (d) none of these

The coordinates (2, 3) and (1, 5) are the foci of an ellipse which passes through the origin. Then the equation of the (a)tangent at the origin is (3sqrt(2)-5)x+(1-2sqrt(2))y=0 (b)tangent at the origin is (3sqrt(2)+5)x+(1+2sqrt(2)y)=0 (c)tangent at the origin is (3sqrt(2)+5)x-(2sqrt(2)+1))y=0 (d)tangent at the origin is (3sqrt(2)-5)x-y(1-2sqrt(2))=0

The coordinates (2, 3) and (1, 5) are the foci of an ellipse which passes through the origin. Then the equation of the (a)tangent at the origin is (3sqrt(2)-5)x+(1-2sqrt(2))y=0 (b)tangent at the origin is (3sqrt(2)+5)x+(1+2sqrt(2)y)=0 (c)tangent at the origin is (3sqrt(2)+5)x-(2sqrt(2+1))y=0 (d)tangent at the origin is (3sqrt(2)-5)-y(1-2sqrt(2))=0

The points on the line x=2 from which the tangents drawn to the circle x^2+y^2=16 are at right angles is (are) (a) (2,2sqrt(7)) (b) (2,2sqrt(5)) (c) (2,-2sqrt(7)) (d) (2,-2sqrt(5))

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertices. The radius of the circle is a) 2-sqrt(2) b) sqrt(2)-1 c) 1//2 d) 1/(sqrt(2))

C_1 is a circle of radius 1 touching the x- and the y-axis. C_2 is another circle of radius greater than 1 and touching the axes as well as the circle C_1 . Then the radius of C_2 is (a) 3-2sqrt(2) (b) 3+2sqrt(2) (c) 3+2sqrt(3) (d) none of these