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Find the equations of the circles touchi...

Find the equations of the circles touching y-axis at (0,3) and making an intercept of 8 units on the x-axis.

A

`x^(2) + y^(2) pm 10 x - 6y + 9 = 0`

B

`x^(2) + y^(2) pm 6x - 10 y + 9 = 0`

C

`x^(2) + y^(2) -8 x pm 10 y + 9 = 0`

D

`x^(2) + y^(2) + 10 x pm 6y + 9 = 0`

Text Solution

Verified by Experts

The correct Answer is:
A
Given equation of circle touch the Y-axis at(0,3).
In `triangle AOB, r = sqrt(3^(2) + 4^(2)) = 5`

The point (0, 3) and radius 5 satisfies the equation
`x^(2) + y^(2) pm 10x - 6y + 9 = 0.`
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Knowledge Check

  • The equation of a circle touching x-axis at (-4, 0) and cutting off an intercept of 6 units on y-axis can be

    A
    `x^(2) + y^(2) + 8x + 12y + 16 = 0`
    B
    `x^(2) + y^(2) + 8x - 12y + 16 = 0`
    C
    `x^(2) + y^(2) + 8x + 10 y + 16 = 0`
    D
    `x^(2) + y^(2) + 8x - 10y + 16 = 0`

  • Equations of circle which touch y-axis at (0, 3) and intercepts a length of 8 units on the x-axis is

    A
    `x^(2)+y^(2) +10x -6y+9=0`
    B
    `x^(2)+y^(2)+6x-10y+9=0`
    C
    `x^(2)+y^(2) +8x +4y+2=0`
    D
    `x^(2)+y^(2) -10x -6y +9=0`

  • Equation of a circle which touches y-axis at (0,2) and cuts ff an intercept of 3 units from the x-axis is x ^(2) + y ^(2) - 2 alpha x -4y + 4=0 where alpha ^(2)=

    A
    `5//2`
    B
    `25//4`
    C
    `4//25`
    D
    `29`

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