JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If tangents are drawn to the ellipse \(x^2 + 2y^2 = 2\) at all points on the ellipse other than its four vertices than the mid points of the tangents intercepted between the coordinate axes lie on the curve
- A \(\frac{1}{{4{x^2}}} + \frac{1}{{2{y^2}}} = 1\)
- B \(\frac{{{x^2}}}{4} + \frac{{{y^2}}}{2} = 1\)
- C \(\frac{1}{{2{x^2}}} + \frac{1}{{4{y^2}}} = 1\)
- D \(\frac{{{x^2}}}{2} + \frac{{{y^2}}}{4} = 1\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{{2{x^2}}} + \frac{1}{{4{y^2}}} = 1\)
Step-by-step Solution
Detailed explanation
equation of tangent is \(\frac{x}{a}\cos \theta + \frac{y}{b}\sin \theta = 1\) \(A\) is \(\left( {\frac{a}{{\cos \theta }},0} \right)\) \(B\) is \(\left( {0,\frac{b}{{\sin \theta }}} \right)\) Let \(P\left( {h,k} \right)\) is mid point \(2h = \frac{a}{{\cos \theta }}\)…
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