TS EAMCET · Maths · Ellipse
If \(4 x+y+p=0(p>0)\) is a tangent to the ellipse \(x^2+3 y^2=3\) and \(16 x+q y+14=0(q>0)\) is a normal to the ellipse \(x^2+8 y^2=33\), then \(p+q=\)
- A 8
- B 5
- C 9
- D 6
Answer & Solution
Correct Answer
(A) 8
Step-by-step Solution
Detailed explanation
If a line \(y=m x+c\) is tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\), then \(c^2=a^2 m^2+b^2\) \(\therefore 4 x+y+p=0\) or \(y=-4 x-p\) will be tangent to the ellipse \(x^2+3 y^2=3\) or \(\frac{x^2}{3}+\frac{y^2}{1}=1\), then…
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