MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: Upto college level
        

find ind the equation of the circle which pass through the focus of the parabola x^2=4ay and touches it at point (6,9)

8 years ago

Answers : (2)

gOlU g3n|[0]uS
42 Points
							

242_21222_1.jpg

8 years ago
vikas askiitian expert
509 Points
							

x2 = 4ay    ...........1

since circle touches the parabola at (6,9) so this point will satisfy the equation of both the curves

so , from eq 1

 36 = 36a

  a=1 , so eq 1 becomes

x2 = 4y            

now differentiating above eq       

2x = y1 = m (slope of tangent)

at (6,9) , m = 3        ..........2

let (h,k) be the center then slope of line passing through center of circle & the point of contact is given by

  m1 = (k-9)/(h-6)        .........3

mm1 = -1   or

(k-9)/(h-6) . 3 = -1        

 h + 3k = 33                      ................4

now focus of parabola is (0,1) ....

eq of circle is x2+y2 +2gx+2fy+c = 0                              (g=-h , f=-k)

 so eq of circle : x2+y2-2hx-2ky+c      

this circle passes through (0,1) & (6,9) so its eq will satisfy these points therefore

-2k+1+c = 0            ...................5

-12h-18k+117+c = 0             ....................6

from 5 & 6

3h+4k=29          ............7

solving 4 & 7 we get

(h,k) = (-9,14)

c = 27

now required eq of circle is

x2 + y2 18x - 28y + 27 = 0

8 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 728 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details