Q1 If length of major axis intercepted between tangent and normal at a point (acosθ ,bsinθ ) on the ellipse x2/a2 +y2/b2=1 is equal to semi major axis,prove that eccentricity is (secθ (secθ -1))1/2
i am unable to reach the ans... :(
Q2 Show that ellipse x2/a2 +y2/b2=1 ,four normals can not be drawn through a point (h,0) unless lhl<ae2 , e=eccenticity of ellpse
I got a 2nd degree eqn..so how four normals ??
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1 Answers
29Intercept made by the tangenton the x-axis... = \frac{a}{cos\theta }
Intercept made by the normal on the x-axis = \frac{(a^{2} - b^{2})cos\theta }{a}
so acc. to question \frac{a}{cos\theta }-\frac{(a^{2} - b^{2})cos\theta }{a} = \left|a \right|
Solving the abv equation u will get two values of e ..one of them satisfies the question given...
