Home
Class 12
MATHS
Find the equations of the circles passin...

Find the equations of the circles passing through the point `(-4,3)` and touching the lines `x+y=2` and `x-y=2`

Text Solution

Verified by Experts

Since circles touch the lines `x+y=2` and `x-y=2`, centre lies on x-acis or y-axis.
But circle passes through the point `Q(-4,3)`. So, centre lies on negative x-axis.
Let the centre be C(h,0).

Also, radius, `CP=` distance of centre from the line `x-y=0` ( or `x+y-2=0)`
`=(|h-0-2|)/(sqrt(1^(2)+(-1)^(2)))=(|h-2|)/(sqrt(2))`
Also, radius, `CQ=sqrt((h+4)^(2)+(k-3)^(2))`
`:. CQ=CP`
`implies ((h-2)^(2))/(2)=(h+4)^(2)+(0-3)^(2)`
`implies h=(-20+-sqrt(20^(2)-4(46)))/(2)`
`implies h= -10+-3sqrt(6)`
Thus, equation of the circle is `(x-h)^(2)+y^(2)=((h-2)^(2))/(2)`, where `h= -10+- 3sqrt(6)`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CENGAGE ENGLISH|Exercise Examples|13 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 4.1|1 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Matrix|4 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the circle passing through the point (2, 8), touching the lines 4x-3y-24=0 and 4x+3y-42=0 andhaving x-coordinate of the centre of the circle numerically less than or equal to 8.

Find the equation of the circle passing through the point ( 2, 3) and touching the line 2x+3y=4 at the point ( 2, 0)

Find the equation of the circle passing through the points A(4,3). B(2,5) and touching the axis of y. Also find the point P on the y-axis such that the angle APB has largest magnitude.

Find the equation of circle passing through the points (1,-2) and (3,-4) and touches the X-axis.

Find the equation of the circle passing through (-1,0) and touching x+ y-7 = 0 at (3,4)

Find the gradient of the line passing through the point (2,8) and touching the curve y=x^3.

Find the equations of the lines passing through the point (4,5) parallel to lines 3x=4y+7 .

Find the equation of the circle passing through the point of intersection of the lines x+3y=0\ a n d\ 2x-7y=0 and whose centre is the point of intersection of the lines x+y+1=0\ a n d\ x-2y+4=0.

Find the equation of a line passing through the point (2,3) and parallel to the line 3x-4y+5=0 .

Find the equation of circle passing through the point (2,3) and (-1,1) and whose centre is on the line x - 3y - 11 = 0