A circle passes through (−2, 4) and touches the y - axis at (0, 2).  Which one of the following equations can represent a diameter of this circle ?

  • Option 1)

    4x + 5y - 6 = 0

  • Option 2)

    2x - 3y + 10 = 0

  • Option 3)

    3x + 4y - 3 = 0

  • Option 4)

    5x + 2y + 4 = 0

 

Answers (1)

As we learnt in 

Family of circle -

S+KL= 0

- wherein

Equation of the family of circles passing through point of intersection S=0 \, and\, line\, L=0.

 Using Family of circles equation is 

\left ( x-0 \right )^2 +\left ( y-2 \right )^2+\lambda x=0

Since circle touches x=0 at the point \left ( 0,2 \right )

we get, x^2+y^2-4y+\lambda x+4=0

It passes through \left ( -2, 4 \right )

Thus,      4+4-2\lambda =0

\lambda =4

equation of circle is 

x^2+y^2-4y+4x+4=0


Option 1)

4x + 5y - 6 = 0

Incorrect

Option 2)

2x - 3y + 10 = 0

Correct

Option 3)

3x + 4y - 3 = 0

Incorrect

Option 4)

5x + 2y + 4 = 0

Incorrect

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