InterviewSolution
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InterviewSolution
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Show that the line x+y-2=0 touches the Parabola x^2=-8y. Find the co-ordinate of the point of contact. |
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Answer» ANSWER: ( 4 , - 2 ) We know that , The tangency condition of parabola is c = a/m Given line → x + y - 2 = 0 Here c = - 2 and m = -1 Parabola → x2 = - 8y a = 2 a/m = 2/-1 = -2 Hence c = a/m \(\therefore\) x + y - 2 = 0 is a tangent to the parabola x2 = - 8y . The equation of tangent at point ( x1 , y1 ) to the parabola x2 = - 8y is xx1 = -4( y + y1 ) xx1 = -4y - 4y1 xx1 + 4y + 4y1 = 0 comparing the above equation with x + y - 2 = 0 x1 = 4 = - 2y1 x1 = 4 y1 = - 2 \(\therefore\) The coordinates point of contact are ( 4 , - 2 ). |
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