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

  • 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 having centre at (3,-4) and touching the line 5x+12 y-12=0.

Find the equation of the circle having centre at (3,-4) and touching the line 5x+12 y-12=0.

Find the equation of the circle which has centre C (3, 1) and which touches the line 5x-12y + 10 = 0.

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 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 the circle with centre (3, 4) and touching y- axis.

The equation of the circle whose center is (3,-2) and which touches the line 3x - 4y + 13 = 0 is

Find the equation of the circle passing through (1,2) and which is concentric with the circle x^2+y^2+11x-5y+3=0.

Find the equation of the circle which has its centre at the point (3,4) and touches the straight line 5x+12 y-1=0.