Circle And System Of Circles Question 70
Question: Give the number of common tangents to circle $ x^{2}+y^{2}+2x+8y-23=0 $ and $ x^{2}+y^{2}-4x-10y+9=0 $
[Orissa JEE 2005]
Options:
A) Straight line
B) Circle.
C) Parabola is a U-shaped curve where any point is at an equal distance from a fixed point called the focus and a fixed straight line called the directrix. It is the graph of a quadratic function and is symmetric about its axis of symmetry. The standard form of a parabola is y = ax² + bx + c, where a, b, and c are constants.
D) Ellipse is a closed curve with two foci, where the sum of the distances from any point on the curve to the two foci is constant.
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=-\frac{\beta }{\alpha }x+\beta $ touches the circle, \ $ {{\beta }^{2}}=a^{2}( 1+\frac{{{\beta }^{2}}}{{{\alpha }^{2}}} ) $
therefore $ \frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}}=\frac{1}{a^{2}} $ \ Locus of $ ( \frac{1}{\alpha },\frac{1}{\beta } ) $ is $ x^{2}+y^{2}={{( \frac{1}{a} )}^{2}} $ .
BETA
