If a number of ellipses whose major axis is x-axis and the minor axis is y-axis be described having the same length of the major axis as 2 but a…

Question

If a number of ellipses whose major axis is x-axis and the minor axis is y-axis be described having the same length of the major axis as 2 but a variable minor axis, then the tangents at the ends of their latus rectum pass through fixed points whose distance from the centre is equal to

MARKS Content Team · Accepted Answer

Correct answer: (B) 1 unit. Since the minor axis is variable, hence e is a variable quantity Therefore the equation of the tangent to the ellipse can be written as xae/(a^2)+(yb^2)/(ab^2)=1 ⇒ex+y=a⇒y-a+ex=0 This line passes through the fixed point 0,a (where a=1) Hence, distance fro the centre of the ellipse =1

If a number of ellipses whose major axis is $x$ -axis and the minor axis is $y$ -axis be described having the same length of the major axis as $2$ but a variable minor axis, then the tangents at the ends of their latus rectum pass through fixed points whose distance from the centre is equal to

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