Let the tangent to the parabola y 2 = 12x at the point (3, 
) be perpendicular to the line 2x + 2y = 3. Then the square of distance of the point (6, - 4) from the normal to the hyperbola 
2 x 2 - 9y 2 = 9 
2 at its point ( 
-1, 
+ 2) is equal to.............
Text Solution
Verified by Experts116
(116)
Given,
The tangent to the parabola y 2 = 12x at the point (3, 
) be perpendicular to the line 2x + 2y = 3
So, Slope of tangent 
So, equation of hyperbola will be,
36x 2 - 9y 2 = 324
Now equation of tangent at (5, 8) will be,
So, slope of normal= 
Now finding, equation of normal 
5y- 40 = -2x+ 10
5y + 2x = 50
Now finding, distance from (6, - 4), we get,
Hence, 
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