Two circles with equal radii are intersecting at the points $(0, 1)$ and $(0, -1)$. The tangent at the point $(0, 1)$ to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is :
- $1$
- $\sqrt{2}$
- $ 2 \sqrt{2}$
- $2$
The Correct Option is D
Solution and Explanation
The correct option is(D): 4.
\(DC_1=\frac{\sqrt{2}r}{2}\)
\(=1+\frac{r^2}{2}=r^2\)
\(r=\sqrt2\)
\(C_1C_2=2\)
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Concepts Used:
Conic Sections
When a plane intersects a cone in multiple sections, several types of curves are obtained. These curves can be a circle, an ellipse, a parabola, and a hyperbola. When a plane cuts the cone other than the vertex then the following situations may occur:
Let ‘β’ is the angle made by the plane with the vertical axis of the cone
- When β = 90°, we say the section is a circle
- When α < β < 90°, then the section is an ellipse
- When α = β; then the section is said to as a parabola
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