MHT CET · Maths · Straight Lines
The equation of a line passing through \((\rho \cos \propto, p \sin \propto)\) and making an angle \((90+\propto)\) with positive direction of \(\mathrm{X}\)-axis is
- A \(x \cos \propto-y \sin \propto=2 p\)
- B \(x \sin \propto+y \cos \propto=p\)
- C \(x \cos \propto+y \sin \propto=p\)
- D \(\mathrm{x} \cos \propto+\mathrm{y} \sin \propto=3 \mathrm{p}\)
Answer & Solution
Correct Answer
(C) \(x \cos \propto+y \sin \propto=p\)
Step-by-step Solution
Detailed explanation
Slope of line \(=\tan (90+\propto)=-\cot \propto\)
Equation of required line is
\(
\begin{aligned}
& (y-p \sin \propto)=\frac{-\cos \propto}{\sin \propto}(x-p \cos \propto) \\
& \therefore(\sin \propto) y-p \sin ^2 \propto=(-\cos \propto) x+p \cos ^2 \propto \\
& \therefore(\operatorname{Cos} \propto) x+(\sin \propto) y=p
\end{aligned}
\)
Equation of required line is
\(
\begin{aligned}
& (y-p \sin \propto)=\frac{-\cos \propto}{\sin \propto}(x-p \cos \propto) \\
& \therefore(\sin \propto) y-p \sin ^2 \propto=(-\cos \propto) x+p \cos ^2 \propto \\
& \therefore(\operatorname{Cos} \propto) x+(\sin \propto) y=p
\end{aligned}
\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If the plane \(\frac{x}{2}+\frac{y}{3}+\frac{z}{6}=1\) cuts the co - ordinate axes at points \(A, B, C\) respectively, then area of the triangle ABC isMHT CET 2025 Easy
- The statement pattern is a logically equivalent toMHT CET 2017 Easy
- If \(\bar{a}, \bar{b}, \bar{c}\) are three vectors such that \(\overline{|a|}=3, \overline{|b|}=5, \overline{|c|}=7\) then \(|\bar{a}-\bar{b}|^2+|\bar{b}-\bar{c}|^2+|\bar{c}-\bar{a}|^2\) does not exceedMHT CET 2025 Medium
- In a \(\Delta \mathrm{ABC}\) if \(2 \cos \mathrm{C}=\operatorname{Sin} \mathrm{B} .\) CosecA, thenMHT CET 2020 Easy
- Let \(A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]\) and \(B=\left[\begin{array}{l}4 \\ 0 \\ 2\end{array}\right]\) such that \(\mathrm{AX}=\mathrm{B}\), then \(\mathrm{X}=\)MHT CET 2024 Easy
- If \(\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\bar{c}=3 \hat{i}+\lambda \hat{j}+5 \hat{k}\) are coplanar, then \(\lambda\) is the root of the equationMHT CET 2021 Easy
More PYQs from MHT CET
- If \(\int \frac{2 x+3}{(x-1)\left(x^2+1\right)} \mathrm{d} x=\log _e\left\{(x-1)^{\frac{5}{2}}\left(x^2+1\right)^a\right\}-\frac{1}{2} \tan ^{-1} x+\mathrm{A}\) where \(A\) is an arbitrary constant, then the value of \(a\) isMHT CET 2025 Medium
- If the differential equation \(\frac{d y}{d x}+\frac{x}{y}=\frac{a}{y}\) where \(a\) is constant, represents a family of circles then the radius of the circle is ......MHT CET 2025 Medium
- What is the number of moles of \(\mathrm{sp}^2\) hybrid carbon atoms present in \(\mathrm{n}\) moles of isopentane?MHT CET 2023 Medium
- \(\int \frac{1+\sin (\log x)}{1+\cos (\log x)} \mathrm{d} x=\)MHT CET 2024 Medium
- Volume of a balloon at \(25^{\circ} \mathrm{C}\) and 1 bar pressure is \(2 \cdot 27 \mathrm{~L}\). If the pressure of the gas in balloon is reduced to \(0.227\) bar, what is the rise in volume of a gas?MHT CET 2020 Easy
- Given below is diagram of T. S of testis. Select the option which gives correct identification of function of cells labeled A, B, C and D from the options given below.
A - cells undergo spermatogenesis to produce spermatozoa.
B - cell responsible for development of male secondary sexual characters.
C - heads of sperms remain attached to these cells.
D - haploid male gamete.MHT CET 2023 Hard