The X and Y intercepts of the tangent to the hyperbola x^2 20 - y ^2 5 =1 which is perpendicular to the line 4 x+3 y=7 , are respectively

Step-by-step solution

To determine the intercepts of the tangent to the hyperbola perpendicular to the line 4x+3y=7 , first note that the slope of the given line is m₁ = - 4 3 . Since the tangent is perpendicular, its slope is m₂ = 3 4 . The standard form of the hyperbola is x^2 20 - y^2 5 = 1 , implying a^2 = 20 and b^2 = 5 . The equation for a tangent with slope m is y = mx a^2 m^2 - b^2 . Substituting m = 3 4 gives y = 3 4 x 20 9 16 - 5 = 3 4 x 45 4 - 20 4 = 3 4 x 5 2 . Two tangents exist: y = 3 4 x + 5 2 and y = 3 4 x - 5 2 . For y