Let P be the point on the parabola, y2=8x which is at a minimum distance from the centre C of the circle, x2 + (y+6)2=1. Then the equation of the circle, passing through C and having its centre at P is :

  • Option 1)

     x2 + y2 − 4x + 8y + 12 = 0

     

  • Option 2)

    x2+y2−x+4y−12=0

     

  • Option 3)

     x^{2}+y^{2}-\frac{x}{4}+2y-24=0

  • Option 4)

    x2 + y2 − 4x + 9y + 18 = 0

     

 

Answers (2)

As we learnt in

Parametric coordinates of parabola -

x= at^{2}

y= 2at

- wherein

For the parabola.

y^{2}=4ax

 

 

Equation of a circle -

\left ( x-h \right )^{2}+\left ( y-k \right )^{2}= r^{2}

- wherein

Circle with centre \left ( h,k \right ) and radius r.

 

 Equation of  normal of y^{2}=4ax in

parametric form y=-tx+2at+at^{3}

If it passes through (0,-6)

\Rightarrow -6=2at+at^{3}

Put a=2

we get t= -1

This point is (a, -2a)   \Rightarrow (2, -4)

Radius of circle = distance between  \left ( 0,-6 \right ) and \left ( 2,-4 \right )

\Rightarrow \sqrt{2^{2}+2^{2}}=2\sqrt{2}

Hence equation is

\left ( x-2 \right )^2+\left ( y+4 \right )^2=\left ( 2\sqrt{2} \right )^2

x^{2}+y^{2}-4x+8y+12=0


Option 1)

 x2 + y2 − 4x + 8y + 12 = 0

 

Correct option

Option 2)

x2+y2−x+4y−12=0

 

Incorrect Option

Option 3)

 x^{2}+y^{2}-\frac{x}{4}+2y-24=0

Incorrect Option

Option 4)

x2 + y2 − 4x + 9y + 18 = 0

 

Incorrect Option

Most Viewed Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 14999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions