Embibe Experts Solutions for Chapter: Parabola, Exercise 4: EXERCISE-4
Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Parabola, Exercise 4: EXERCISE-4
Attempt the free practice questions on Chapter 18: Parabola, Exercise 4: EXERCISE-4 with hints and solutions to strengthen your understanding. Beta Question Bank for Engineering: Mathematics solutions are prepared by Experienced Embibe Experts.
Questions from Embibe Experts Solutions for Chapter: Parabola, Exercise 4: EXERCISE-4 with Hints & Solutions
are the points of contact of the tangents drawn from the point to the parabola . If be the normal to the parabola at then prove that is bisected by the directrix.

The normal at a point to the parabola meets its axis at . is another point on the parabola such that is perpendicular to the axis of the parabola. Prove that constant.

Three normals to pass through the point Show that one of the normals is given by find the equations of the others.

Find the condition on so that the two tangents drawn to the parabola from a point are normals to the parabola

Let is the focus of the parabola and the foot of the directrix, is a double ordinate of the curve and meets the curve again in Prove that passes through focus.

If and be three points on the parabola and the normals at these points meet in a point, then prove that

A variable chord joining points and of the parabola subtends a right angle at a fixed point of the curve. Show that it passes through a fixed point. Also find the co-ordinates of the fixed point.

Show that a circle circumscribing the triangle formed by three co-normal points passes through the vertex of the parabola and its equation is, where is the point from where three concurrent normals are drawn.
