Home
Class 12
MATHS
A circle touches the y-axis at the point...

A circle touches the y-axis at the point (0, 4) and cuts the x-axis in a chord of length 6 units. Then find the radius of the circle.

Text Solution

Verified by Experts

Circles touch the y-axis at point P(0,4).

Intercept QR of circle on x-axis is 6 units
`:. QM =3`
Also, C is centre of one of the circles
`:. CM=4`
In triangle CMQ , we have
`CQ^(2)=QM^(2)+CM^(2)=3^(2)+4^(2)`
`:. CQ=5=CP=` radius
Therefore, centre of the circle lying in first quadrant is C(5,4). Thus, equation of circle is `(x-5)^(2)+(y-4)^(2)=25`.
Equation of circle having centre C(-5,4) in secong quadrant is `(x+5)^(2)+(y-4)^(2)=25`.
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4 . Then find the radius of the circle.

A circle touches the y axis at (0,2) and its x intercept equal to 3 units, then the equation of the circle is

A circle touches the x-axis and also thouches the circle with center (0, 3) and radius 2. The locus of the center of the circle is (a)a circle (b) an ellipse (c)a parabola (d) a hyperbola

If the lines 3x-4y+4=0 and 6x-8y-7=0 are tangents to a circle, then find the radius of the circle.

Find the equation of the circle which is touched by y=x , has its center on the positive direction of the x=axis and cuts off a chord of length 2 units along the line sqrt(3)y-x=0

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4. The radius of the circle is

The equation of radical axis of two circles is x + y = 1 . One of the circles has the ends ofa diameter at the points (1, -3) and (4, 1) and the other passes through the point (1, 2).Find the equating of these circles.

Find the locus of center of circle of radius 2 units, if intercept cut on the x-axis is twice of intercept cut on the y-axis by the circle.

A line 4x-3y+20=0 cuts a chord of length 8 units on a circle with centre at (-2,-1) . Find the equation of the circle.

A variable circle passes through the point A(a ,b) and touches the x-axis. Show that the locus of the other end of the diameter through A is (x-a)^2=4b y .