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If the curves `y^2=6x`, `9x^2+by^2=16` intersect each other at right angles then the value of b is: (1) 6 (2) `7/2` (3) `4` (4) `9/2`A. `6`B. `(7)/(2)`C. `4`D. `(9)/(2)` |
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Answer» Correct Answer - D We have, `y^(2) = 6x ` `rArr " " 2y (dy)/(dx) = 6 rArr (dy)/(dx) = (3)/(y)` Slope of tangent at `(x_1, y_1)` is `m_1 = (3)/(y_1)` Also, ` 9x^(2) + by^(2) = 16` `rArr " " 18 x + 2by (dy)/(dx) = 0 rArr (dy)/(dx) = (-9x)/(by)` Slope of tangent at `(x_1, y_1)` is `m_2` = `(-9x_1)/(by_1)` Since, these are intersection at right angle. `therefore m_1m_2 = -1 rArr = (27x_1)/( by_1^(2)) = 1 ` `rArr " " ( 27 x_1)/( 6bx _1) = 1 " " [ because y_1^(2) = 6x_1]` `rArr " " b = (9)/(2)` |
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