AP EAMCET · Maths · Ellipse
Tangents are drawn from point \((1,1)\) to the ellipse \(S \equiv\) \(x^2+4 y^2-2 x+8 y+1=0\). If \(m_1, m_2\left(m_1>m_2\right)\) are the slopes of these tangents, then with respect to the given ellipse the point \(\mathrm{P}\left(\mathrm{m}_1, \mathrm{~m}_2\right)\)
- A lies inside the ellipse \(S=0\)
- B lies outside the ellipse \(\mathrm{S}=0\)
- C lies on the ellipse \(\mathrm{S}=0\)
- D is the centre of the ellipse \(\mathrm{S}=0\)
Answer & Solution
Correct Answer
(A) lies inside the ellipse \(S=0\)
Step-by-step Solution
Detailed explanation
Given ellipse \(x^2+4 y^2-2 x+8 y+1=0\) \[ \Rightarrow \frac{(x-1)^2}{4}+\frac{(y+1)^2}{1}=1 ...(i)\] ...(i) Let \(m\) be slope of tangent passing through \((1,1)\) on equation (i) Hence \(y-1=m(x-1)\) \(\Rightarrow \quad y=m x+(m-1)\) ...(ii) When \(y=m x+c\) is a tangent to…
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