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 point on the line x=3 from which the tangents drawn to the circle x^(2)+y^(2)=8 are at right angles is

The length of the tangent from the point (4, 5) to the circle x^2 + y^2 + 2x - 6y = 6 is : (A) sqrt(13) (B) sqrt(38) (C) 2sqrt(2) (D) 2sqrt(13)

The point,at shortest distance from the line x+y=10 and lying on the ellipse x^(2)+2y^(2)=6, has coordinates (A) (sqrt(2),sqrt(2)) (B) (0,sqrt(3))(C)(2,1)(D)(sqrt(5),(1)/(sqrt(2)))

Radius of the circle that passes through the origin and touches the parabola y^(2)=4ax 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 image of the centre of the circle x^2 + y^2 = 2a^2 with respect to the line x + y = 1 is : (A) (sqrt(2), sqrt(2) (B) (1/sqrt(2) , sqrt(2) ) (C) (sqrt(2), 1/sqrt(2)) (D) none of these

The abscissa of the point on the curve sqrt(xy)=a+x the tangent at which cuts off equal intercepts from the coordinate axes is -(a)/(sqrt(2))( b) a/sqrt(2)(c)-a sqrt(2)(d)a sqrt(2)

The length of the tangent of the curve y=x^(2)+2 at (1, 3) is (A) sqrt(5) (B) 3sqrt(5) (C) 3/2 (D) (3sqrt(5))/(2)

The length of the tangent of the curve y=x^(2)+2 at (1 3) is (A) sqrt(5) (B) 3sqrt(5) (C) 3/2 (D) (3sqrt(5))/(2)

The length of the tangent of the curve y=x^(2)+2 at (1, 3) is (A) sqrt(5) (B) 3sqrt(5) (C) (3)/(2) (D) (3sqrt(5))/(2)

The equaiton of the line which bisects the obtuse angle between the lines x-2y+4=0 and 4x-3y+2=0 (A) (4-sqrt(5))x-(3-2(sqrt(5)) y+ (2-4sqrt(5))=0 (B) (3-2sqrt(5)) x- (4-sqrt(5))y+ (2+4(sqrt(5))=0 (C) (4+sqrt(5)x-(3+2(sqrt(5))y+ (2+4(sqrt(5))=0 (D) none of these