A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is

a. |
A hyperbola |
b. |
A parabola |

c. |
A straight line |
d. |
An ellipse |

A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is

a. |
A hyperbola |
b. |
A parabola |

c. |
A straight line |
d. |
An ellipse |

1 Answer - 5876 Votes

3537

Let equation of circle is

x^{2} + y^{2} + 2fx + 2fy + e = 0, it passes through (0, 2b)

⇒ 0 + 4b^{2} + 2g × 0 + 4f + c = 0

⇒ 4b^{2} + 4f + c = 0 ...(i)

2 = 4a ….(ii)

g^{2} − c = 4a^{2}

⇒ c = (g^{2} − 4a^{2})

Putting in equation (1)

⇒ 4b^{2} + 4f + g^{2} − 4a^{2} = 0

⇒ x^{2}+4y+4(b^{2 }− a^{2}) = 0, it represent a parabola.