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From an external point `P ,`a pair of tangents is drawn to the parabola `y^2=4xdot`If `theta_1a n dtheta_2`are the inclinations of these tangents with the x-axis such that `theta_1+theta_2=pi/4`, then find the locus of `Pdot`A. `x - y +1 = 0`B. `x +y - 1 = 0`C. `x - y - 1 = 0`D. `x +y + 1 = 0` |
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Answer» Correct Answer - C Equation of tangent having slope m is `y = mx +(1)/(m)`, which passes through the point (h,k). `:. m^(2) h - mk +1 =0` `:. m_(1) + m_(2) = (k)/(h), m_(1)m_(2) = (1)/(h)` Given `theta_(1) + theta_(2) = (pi)/(4)` `rArr (m_(1)+m_(2))/(1-m_(2)m_(2)) =1` `rArr (k)/(h) =1 -(1)/(h)` `rArr y = x-1` |
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