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JEE Main202127 Jul 2021Evening ShiftMathematicsEllipseActual

Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its centre at 3 , - 4 , one focus at 4 , - 4 and one vertex at 5 , - 4 . If m x - y = 4 , m > 0 is a tangent to the ellipse E , then the value of 5 m 2 is equal to _____ .

Correct answer

0

Step-by-step solution

We know that, If the standard ellipse is shifted to have center h ,   k , then it's equation is x - h 2 a 2 + y - k 2 b 2 = 1 The center is C h ,   k The vertices on the major axis are A h + a ,   k and A ' h - a ,   k The foci are S h + a e ,   k and S ' h - a e ,   k The eccentricity e = a 2 - b 2 a 2 Given C 3 , - 4 , S 4 , - 4 and A 5 , - 4 Therefore, h ,   k = 3 ,   - 4 h + a ,   k = 5 ,   - 4 h + a e ,   k = 4 ,   - 4 Clearly, a = 2   &

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