Home
Class 12
MATHS
Find the equation of the circle having c...

Find the equation of the circle having center at (2,3) and which touches `x+y=1`

Text Solution

Verified by Experts

The centre of the circle is `C (2,3)`.

Also, line `x+y-1=0` is tangent to the circle.
Hence, the radius of the circle is the perpendicular distance of centre from the tangent.
Therefore, radius `r=CP=(|2+3-1|)/(sqrt(1^(2)+1^(2)))=2sqrt(2)`
Hence, the equation of circle is `(x-2)^(2)+(y-3)^(2)=8`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Find the equation of the circle having radius 5 and which touches line 3x+4y-11=0 at point (1, 2).

Find the equation of the circle with center at (3,-1) and which cuts off an intercept of length 6 from the line 2x-5y+18=0

Find the equation of circle centred at (3,3) and touches the coordinate axes.

Find the equation of the circle which touch the line 2x-y=1 at (1,1) and line 2x+y=4

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

Find the equation of the circle whose radius is 5a n d which touches the circle x^2+y^2-2x-4y-20=0 externally at the point (5,5)dot

Find the equation of the circle which touches both the axes and the line x=c

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

Find the equation of a circle with center (4, 3) touching the circle x^2+y^2=1

Find the equation of the circle which touches the x-axis and whose center is (1, 2).