Download App

Tangents and Normals — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTangents and Normals3 Marks
Question
Write the angle between the curves $y^2 = 4x$ and $x^2 = 2y - 3$ at the point $(1, 2)$.
✓

Answer

Given:
$y^2 = 4x$ ...(1)
$x^2 = 2y − 3$ ...(2)
On differentiating (1) w.r.t.x, we get
$2\text{y}\frac{\text{dy}}{\text{dx}}=4$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{2}{\text{y}}$
$\Rightarrow\text{m}_1=\Big(\frac{\text{dy}}{\text{dx}}\Big)_{(1,2)}=\frac{2}{2}=1$
On differentiating (2) w.r.t.x, we get
$2\text{x}=2\frac{\text{dy}}{\text{dx}}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\text{x}$
$\Rightarrow\text{m}_2=\Big(\frac{\text{dy}}{\text{dx}}\Big)_{(1,2)}=1$
Thus, we get
$\tan\theta=\Big|\frac{\text{m}_1-\text{m}_2}{1+\text{m}_1\text{m}_2}\Big|$
$\Rightarrow\tan\theta=\Big|\frac{1-1}{1+1}\Big|$
$\Rightarrow\tan\theta=0$
$\Rightarrow\theta=0$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from Tangents and Normals→Tangents and Normals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
→
Solve: $3 e^x \tan y d x+\left(1+e^x\right) \sec ^2 y d y=0$. Also, find the particular solution when $x=0$ and $y=\pi$.
→
Evaluate :

$\int_0^\pi \frac{1}{3+2 \sin x+\cos x} \cdot d x$

→
Two coins are tossed once. Find $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$ in each of the following:
A = Tail appears on one coin,
B = One coin shows head.
→
$\int \text{(2x} - 3)^{5} + \sqrt{3\text{x + 2}}\text{ dx}$
→
Diffrentiate the following w. r. t. x.

$\cot ^{-1}\left(\frac{1+35 x^2}{2 x}\right)$

→
Evaluate the following integrals:$\int\frac{\sin\text{x}-\cos\text{x}}{\sqrt{\sin2\text{x}}}\text{ dx}$
→
Find the angle between the lines $2\text{x}=3\text{y}=-\text{z}$ and $6\text{x}=-\text{y}=-4\text{z}.$
→
Evaluate the following definite integrals:$\int_{1}^\limits{\text{e}}\frac{\log\text{x}}{\text{x}}\text{ dx}$
→
For each of the following differential equations, find the particular solution satisfying the given condition:

$\left(x-y^2 x\right) d x-\left(y+x^2 y\right) d y=0$, when $x=2, y=0$

→