Shoe that the length of the chord of contact of tangents drawn from `(x_1,y_1)`, to the parabola `y^2=4ax` is `1/asqrt((y_1^2-4ax_1)(y_1^2+4a^2))`

Shoe that the length of the chord of contact of tangents drawn from (x_(1),y_(1)), to the parabola y^(2)=4ax is (1)/(a)sqrt((y_(1)^(2)-4ax_(1))(y_(1)^(2)+4a^(2)))

Show that the length of the chord of contact of the tangents drawn from (x_(1),y_(1)) to the parabola y^(2)=4ax is (1)/(a)sqrt((y_(1)^(2)-4ax_(1))(y_(1)^(2)+4a^(2)))

The equation of the chord of contact of tangents from (1,2) to the hyperbola 3x^(2)-4y^(2)=3 , is

Area of the triangle formed by the tangents from (x_(1),y_(1)) to the parabola y^(2)=4ax and its chord of contact is ((y_(1)^(2)-4ax_(1))^((3)/(2)))/(2a)=(S_(11)^((3)/(2)))/(2a)

What is the focal distance of any point P(x_(1), y_(1)) on the parabola y^(2)=4ax ?

The locus of the poles of tangents to the parabola y^(2)=4ax with respect to the parabola y^(2)=4ax is

If the chord of contact of tangents from a point P to the parabola y^(2)=4ax touches the parabola x^(2)=4by, then find the locus of P.

A point P moves such that the chord of contact of the pair of tangents from P on the parabola y^(2)=4ax touches the rectangular hyperbola x^(2)-y^(2)=c^(2). Show that the locus of P is the ellipse (x^(2))/(c^(2))+(y^(2))/((2a)^(2))=1