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If the line y=mx+c touches the parabola `y^(2)=4a(x+a)`, thenA. `c=a+a/m`B. `c=am+a/m`C. `c=am+a`D. none of these |
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Answer» Correct Answer - B The equation of the parabola is `y^(2)=4a(x+6)" …(i)"` The equation of the line `y = mx + c` can be written as `y=m(x+a)+c-am" …(ii)"` we know that the line` y=mc+lamda` touches the parabola `y^(2)=4ax`, if `lamda=a/m`. Therefore, line (ii) will touch the parabola (i), if `c-am=a/mrArrc=am+a/m` ALITER The y=mx+c will touch the parabola `y^(2)=4a(x+a)` if the quadratic equation `(mx+c)^(2)=4a(x+a)` has equal roots i.r. its discireminant is equal to zero. `:." "4(mc-2a)^(2)-4m^(2)(c^(2)-4a^(2))rArrc=am+a/m` |
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