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36. The equation of common tangent to y2 = 4ax and x2=4ay is37. Parabola P always passes through the points |
Answer» 36.The equation of any tangent to y2=4ax is y=mx+ma If it touches x2=4ay then, the equation. ⇒x2=4a(mx+ma) has equal roots. ⇒mx2−4am2x−4a2=0 has equal roots If the roots are equal, the discriminant is equal to 0 i.e.,b2−4ac=0 ⇒16a2m4+16a2m=0 ⇒16a2m4=−16a2m m=−1 Putting m=−1 in y=mx+am we get, y=−x−a ⇒x+y+a=0 This is the common tangent to the two parabola. 37. option D (-a, 0), (0, a) |
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