Question Number 93853 by Ar Brandon last updated on 15/May/20
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{at}\:\mathrm{which}\:\mathrm{the}\:\mathrm{parabola} \\ $$$$\mathrm{y}=\mathrm{x}^{\mathrm{2}} \:\mathrm{cuts}\:\mathrm{through}\:\mathrm{the}\:\mathrm{line}\:\mathrm{3x}−\mathrm{y}−\mathrm{2}=\mathrm{0} \\ $$
Answered by Kunal12588 last updated on 15/May/20
$${y}={x}^{\mathrm{2}} ,\:{y}=\mathrm{3}{x}−\mathrm{2} \\ $$$$\left(\mathrm{1},\mathrm{1}\right)\:{and}\:\left(\mathrm{2},\mathrm{4}\right)\:{intersection} \\ $$$${at}\:\left(\mathrm{1},\mathrm{1}\right) \\ $$$$\angle={tan}^{−\mathrm{1}} \mid\frac{\mathrm{2}\left(\mathrm{1}\right)−\mathrm{3}}{\mathrm{1}+\mathrm{2}\left(\mathrm{1}\right)×\mathrm{3}}\mid={tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{7}} \\ $$$${at}\:\left(\mathrm{2},\mathrm{4}\right) \\ $$$$\angle={tan}^{−\mathrm{1}} \mid\frac{\mathrm{2}\left(\mathrm{2}\right)−\mathrm{3}}{\mathrm{1}+\mathrm{2}\left(\mathrm{2}\right)×\mathrm{3}}\mid={tan}^{−\mathrm{1}} \frac{\mathrm{4}}{\mathrm{13}} \\ $$
Commented by Ar Brandon last updated on 15/May/20
thanks ��
Commented by Kunal12588 last updated on 15/May/20
I belive you already knew the answer;
anyway you are welcome.
Commented by Ar Brandon last updated on 15/May/20
No madame. Your solution was of great help. I'm just laughing at myself.��
Commented by Kunal12588 last updated on 16/May/20
I am male.
Commented by Ar Brandon last updated on 17/May/20
OK bro ��