iran-konkur 2023 Q18

iran-konkur · Other · konkur-riazi_1402_general Tangents, normals and gradients Common tangent line to two curves
18 -- Line $d$ is tangent to the parabola $y = x^2 + 1$, cuts the $x$-axis at two points, and the tangent lines drawn at those two points are perpendicular to each other. What are the coordinates of the $x$-intercept of line $d$?
(1) $1/25$ (2) $3/25$ (3) $\circ/75$ (4) $2/75$
\textbf{18 --} Line $d$ is tangent to the parabola $y = x^2 + 1$, cuts the $x$-axis at two points, and the tangent lines drawn at those two points are perpendicular to each other. What are the coordinates of the $x$-intercept of line $d$?

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(1) $1/25$ \hfill (2) $3/25$ \hfill (3) $\circ/75$ \hfill (4) $2/75$

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