Let the tangent to the parabola y 2 = 12 x at the point 3 , α be perpendicular to the line 2 x + 2 y = 3 . Then the square of distance of the point 6 , - 4 from the normal to the hyperbola α 2 x 2 - 9 y 2 = 9 α 2 at its point

Question

Let the tangent to the parabola y 2 = 12 x at the point 3 , &#945; be perpendicular to the line 2 x + 2 y = 3 . Then the square of distance of the point 6 , - 4 from the normal to the hyperbola &#945; 2 x 2 - 9 y 2 = 9 &#945; 2 at its point &#945; - 1 , &#945; + 2 is equal to .............

Quantrex Academy · Accepted Answer

Correct answer: 0

Given, The tangent to the parabola y 2 = 12 x at the point 3 , &#160; &#945; be perpendicular to the line 2 x + 2 y = 3 So, Slope of tangent = 1 = 6 &#945; &#8658; &#945; = 6 So, equation of hyperbola will be, 36 x 2 - 9 y 2 = 324 &#8658; x 2 9 - y 2 36 = 1 Now equation of tangent at 5 , 8 will be, 5 x 9 - 8 y 36 = 1 &#8658; 5 x - 2 y = 9 So, slope of normal = - 2 5 Now finding, equation of normal y - 8 = - 2 5 x - 5 &#8658; 5 y - 40 = - 2 x + 10 &#8658; 5 y + 2 x = 50 Now finding,distance from 6 , &#160; - 4 , we

Let the tangent to the parabola y 2 = 12 x at the point 3 , α be perpendicular to the line 2 x + 2 y = 3 . Then the square of distance of the point 6 , - 4 from the normal to the hyperbola α 2 x 2 - 9 y 2 = 9 α 2 at its point α - 1 , α + 2 is equal to .............

Correct answer

Step-by-step solution

More from Hyperbola

Let the tangent to the parabola y 2 = 12 x at the point 3 , &#945; be perpendicular to the line 2 x + 2 y = 3 . Then the square of distance of the point 6 , - 4 from the normal to the hyperbola &#945; 2 x 2 - 9 y 2 = 9 &#945; 2 at its point &#945; - 1 , &#945; + 2 is equal to .............

Correct answer

Step-by-step solution

More from Hyperbola

Let the tangent to the parabola y 2 = 12 x at the point 3 , α be perpendicular to the line 2 x + 2 y = 3 . Then the square of distance of the point 6 , - 4 from the normal to the hyperbola α 2 x 2 - 9 y 2 = 9 α 2 at its point α - 1 , α + 2 is equal to .............