AP EAMCET202316 May 2023Evening ShiftMathematicsHyperbolaActual

If the equation of the tangent drawn at (h, k) to the hyperbola ( x -1)^2 1 - ( y -2)^2 2 =1 is x =2 , then h + k =

Options

Correct answer

B. 4

Step-by-step solution

Given equation of hyperbola is aligned & (x-1)^2 1 - (y-2)^2 2 =1 ... (i) & 2(x-1)-(y-2) d y d x =0 d y d x = 2(x-1) y-2 ... (ii) aligned Given equation of tangent is x=2 , so, slope = 1 0 2(x-1) y-2 = 1 0 y=2=k putting in (i), we get ( x -1)^2 1 -0=1 x =2= h Now, h+k=2+2=4

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