Home
Class 12
MATHS
Find the equation of the circle with cen...

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`

Text Solution

Verified by Experts

The correct Answer is:
`(x-3)^(2)+(y+1)^(2)=38`
Let the circle be as shown below.
`CM=(|2(3)-(5(-1)+18)|)/(sqrt(2^(2)+(-5)^(2)))=sqrt(29)`

`:. AC^(2)=AM^(2)+CM^(2)=9+29=38`
`:. ` Radius `=sqrt(38)`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 4.6|6 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 4.7|5 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 4.4|4 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 whose centre is at (3,-1) and which cuts off a chord of length 6u n i t s on the line 2x-5y+18=0.

Find the equation of the circle whose centre is at (3,-1) and which cuts off a chord of length 6u n i t s on the line 2x-5y+18=0.

The equation of the cirlce with centre (0,0) and which cuts off a chord of length 4 units on x+2y=5 is

Lines 5x + 12y - 10 = 0 and 5x - 12y - 40 = 0 touch a circle C1 of diameter 6. If the center of C1, lies in the first quadrant then the equation of the circle C2, which is concentric with C1, and cuts intercept of length 8 on these lines

Find the equation of the circle which passes through the origin and cuts off intercepts -2 and 3 from the coordinate axes .

Find the equation of the straight line which passes though (1,-2)a n d cuts off equal intercepts on the axes.

Slope of a line which cuts off intercepts of equal lengths on the axes is

Slope of a line which cuts off intercepts of equal lengths on the axes is

Find the equation of the line which cuts off an intercept -5 on y-axis and has slope 1/2 .

Find the equation of the circle which passes through the origin and cuts off intercepts 6 and 8 from the positive parts of x and y axes respectively.