﻿ The coordinates of the point on the parabola y2 = 8x which is at minimum distance from the circle x2 + (y + 6)2 = 1 are : Kaysons Education

# The Coordinates Of The Point On The Parabola y2 = 8x which Is At Minimum Distance From The Circle x2 + (y + 6)2 = 1 Are

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### Solution

Correct option is

(2, 4)

Let P (2t2, 4t) be any point on the parabola. The centre of the given circle is O (0, –6) and the radius is 1.

(other roots are imaginary)

Hence OP2 is minimum at t = –1. But if A is any point on the circle and onOP (min), then AP will be minimum when OP is minimum as AP = OP – (radius of circle). Thus the required point is P(2(–1))2, 4(–1) = (2, –4).