JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The locus of mid-points of the line segments joining \((-3,-5)\) and the points on the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\) is :
- A \(9 x^{2}+4 y^{2}+18 x+8 y+145=0\)
- B \(36 x^{2}+16 y^{2}+90 x+56 y+145=0\)
- C \(36 x^{2}+16 y^{2}+108 x+80 y+145=0\)
- D \(36 x^{2}+16 y^{2}+72 x+32 y+145=0\)
Answer & Solution
Correct Answer
(C) \(36 x^{2}+16 y^{2}+108 x+80 y+145=0\)
Step-by-step Solution
Detailed explanation
General point on \(\frac{\mathrm{x}^{2}}{4}+\frac{\mathrm{y}^{2}}{9}=1\) is \(\mathrm{A}(2 \cos \theta, 3 \sin \theta)\) given \(\mathrm{B}(-3,-5)\) \(\text { midpoint } C\left(\frac{2 \cos \theta-3}{2}, \frac{3 \sin \theta-5}{2}\right)\)…
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