Home
Class 11
MATHS
Prove that the length of the intercept o...

Prove that the length of the intercept on the normal at the point `P(a t^2,2a t)` of the parabola `y^2=4a x` made by the circle described on the line joining the focus and `P` as diameter is `asqrt(1+t^2)` .

Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that the length of the intercept on the normal at the point P(at^(2),2at) of the parabola y^(2)=4ax made by the circle described on the line joining the focus and P as diameter is a sqrt(1+t^(2))

The length of the chord intercepted on the line 2x-y+2=0 by the parabola x^(2)=8y is t then t=

Point of intersection of normal at P(t1) and Q(t2)

Show that the normal at a point (at^2_1, 2at_1) on the parabola y^2 = 4ax cuts the curve again at the point whose parameter t_2 = -t_1 - 2/t_1 .

Find the equation of the tangent and normal to the parabola y^2=4a x at the point (a t^2,\ 2a t) .

The normal at t_(1) and t_(2) on the parabola y^(2)=4ax intersect on the curve then t_(1)t_(2)

Find the equation of the circle described on the line segment joining the foci of the parabolas x^2 - 4ay and y^2 = 4a(x-a) as diameter.