Question

Find the points on the curve x2 + y2 − 2x − 3 = 0 at which the tangents are parallel to the x-axis.

Answer 1

Hey, mate here is ur Ans

Common thought:- Any tangent parallel to the x-ais makes an angle of 0 degree with the x-axis. That means slope is 0.
$x {}^{2} + y {}^{2} - 2x - 3 = 0.....1 \\ now \: differentate \: the \: given \: equation \: \\ 2x + 2y(dy \div dx) - 2 = 0 \\ dy \div dx = 1 - x \\ dy \div dx = 0(slope) \\ 1 - x = 0 \\ x = 1 \\ now \: sub \: valve \: of \: x \: in \: equation \: 1 \\ 1 {}^{2} \div y {}^{2} - 2 - 3 = 0 \\ y = + 2 \\ or \\ y = - 2 (not \: possible) \\ so \: points\: are \: (1 \: 2)$