Show that the locus of P where the tangents drawn from P to `x^(2)+y^(2)=a^(2)` are perpendicular to each other is `x^(2)+y^(2)=2a^(2)`

Show that the locus of P where the tangents drawn from P to the circle x^(2)+y^(2)=a^(2) include an angle alpha is x^(2)+y^(2)=a^(2)cosec^(2)(alpha)/2

The tangents drawn from the point P to the ellipse 5x^(2) + 4y^(2) =20 are mutually perpendi­cular then P =

Find the locus of the feet of the perpendiculars drawn from the point (b, 0) on tangents to the circle x^(2) + y^(2) =a^(2)

The locus of a point from which two tangent are drawn to x^2-y^2=a^2 which are inclined at angle (pi)/(4) to each other is

The locus of a point from which two tangent are drawn to x^2-y^2=a^2 which are inclined at angle (pi)/(4) to each other is

Find the angle between tangents drawn from P(2, 3) to the parabola y^(2) = 4x

If the chord of contact of tangents from a point P(h, k) to the circle x^(2)+y^(2)=a^(2) touches the circle x^(2)+(y-a)^(2)=a^(2) , then locus of P is

The equations of the tangents drawn from the origin to the circle x^2 + y^2 - 2px - 2qy + q^2 = 0 are perpendicular if (A) p^2 = q^2 (B) p^2 = q^2 =1 (C) p = q/2 (D) q= p/2

If tangents PA and PB are drawn from P(-1, 2) to y^(2) = 4x then

Show that the locus of the foot of the perpendicular drawn from focus to a tangent to the hyperbola x^2/a^2 - y^2/b^2 = 1 is x^2 + y^2 = a^2 .