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Question Number 93853 by Ar Brandon last updated on 15/May/20

Find the angle at which the parabola  y=x^2  cuts through the line 3x−y−2=0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{at}\:\mathrm{which}\:\mathrm{the}\:\mathrm{parabola} \\ $$$$\mathrm{y}=\mathrm{x}^{\mathrm{2}} \:\mathrm{cuts}\:\mathrm{through}\:\mathrm{the}\:\mathrm{line}\:\mathrm{3x}−\mathrm{y}−\mathrm{2}=\mathrm{0} \\ $$

Answered by Kunal12588 last updated on 15/May/20

y=x^2 , y=3x−2  (1,1) and (2,4) intersection  at (1,1)  ∠=tan^(−1) ∣((2(1)−3)/(1+2(1)×3))∣=tan^(−1) (1/7)  at (2,4)  ∠=tan^(−1) ∣((2(2)−3)/(1+2(2)×3))∣=tan^(−1) (4/(13))

$${y}={x}^{\mathrm{2}} ,\:{y}=\mathrm{3}{x}−\mathrm{2} \\ $$$$\left(\mathrm{1},\mathrm{1}\right)\:{and}\:\left(\mathrm{2},\mathrm{4}\right)\:{intersection} \\ $$$${at}\:\left(\mathrm{1},\mathrm{1}\right) \\ $$$$\angle={tan}^{−\mathrm{1}} \mid\frac{\mathrm{2}\left(\mathrm{1}\right)−\mathrm{3}}{\mathrm{1}+\mathrm{2}\left(\mathrm{1}\right)×\mathrm{3}}\mid={tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{7}} \\ $$$${at}\:\left(\mathrm{2},\mathrm{4}\right) \\ $$$$\angle={tan}^{−\mathrm{1}} \mid\frac{\mathrm{2}\left(\mathrm{2}\right)−\mathrm{3}}{\mathrm{1}+\mathrm{2}\left(\mathrm{2}\right)×\mathrm{3}}\mid={tan}^{−\mathrm{1}} \frac{\mathrm{4}}{\mathrm{13}} \\ $$

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 ��

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