AP EAMCET · Maths · Circle
\(x^2+y^2+2 x+4 y-20=0\) and \(x^2+y^2+6 x-8 y+10=0\) are the given circles. Which one of the following is correct?
- A They intersect orthogonally and will have two common tangents. The length of their common chord is \(\frac{5 \sqrt{3}}{\sqrt{2}}\)
- B They intersect at right angles and will have two common tangents. The length of their common chord is 2
- C They do not intersect orthogonally and will have three common tangents. The length of their direct common tangent is 5
- D They touch each other internally and will have only one common tangent
Answer & Solution
Correct Answer
(A) They intersect orthogonally and will have two common tangents. The length of their common chord is \(\frac{5 \sqrt{3}}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
The equation of given two circles are \[ x^2+y^2+2 x+4 y-20=0 \] and \[ x^2+y^2+6 x-8 y+10=0 \] \[ \because \quad \begin{aligned} 2 g_1 g_2+2 f_1 f_2 & =6-16 \\ & =-10=c_1+c_2 \end{aligned} \] So, circles intersects each other orthogonally and will have two common tangents. Now,…
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