MHT CET · Maths · Straight Lines
If the angle between the lines is \(\frac{\pi^c}{4}\) and slope of one of the lines is \(\frac{1}{2}\), then slope of the other line is
- A 3 or \(-\frac{1}{3}\)
- B 4 or \(-\frac{1}{4}\)
- C 2 or \(-\frac{1}{2}\)
- D 3 or -3
Answer & Solution
Correct Answer
(A) 3 or \(-\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
We have \(\theta=45^{\circ}\) and \(\mathrm{m}_1=\frac{1}{2}\)
\(
\begin{aligned}
& \tan \theta=\left|\frac{\mathrm{m}_1-\mathrm{m}_2}{1+\mathrm{m}_1 \mathrm{~m}_2}\right| \\
& \therefore \quad \tan 45^{\circ}=\left|\frac{\frac{1}{2}-\mathrm{m}_2}{1+\left(\frac{1}{2}\right) \mathrm{m}_2}\right| \Rightarrow\left|\frac{1-2 \mathrm{~m}_2}{2+\mathrm{m}_2}\right|= \pm 1 \\
& \therefore \quad 1-2 \mathrm{~m}_2=2+\mathrm{m}_2 \text { or } 1-2 \mathrm{~m}_2=-2 \\
& \therefore \mathrm{m}_2=\frac{-1}{3} \text { or } \mathrm{m}_2=3
\end{aligned}
\)
\(
\begin{aligned}
& \tan \theta=\left|\frac{\mathrm{m}_1-\mathrm{m}_2}{1+\mathrm{m}_1 \mathrm{~m}_2}\right| \\
& \therefore \quad \tan 45^{\circ}=\left|\frac{\frac{1}{2}-\mathrm{m}_2}{1+\left(\frac{1}{2}\right) \mathrm{m}_2}\right| \Rightarrow\left|\frac{1-2 \mathrm{~m}_2}{2+\mathrm{m}_2}\right|= \pm 1 \\
& \therefore \quad 1-2 \mathrm{~m}_2=2+\mathrm{m}_2 \text { or } 1-2 \mathrm{~m}_2=-2 \\
& \therefore \mathrm{m}_2=\frac{-1}{3} \text { or } \mathrm{m}_2=3
\end{aligned}
\)
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
- The function \(\mathrm{f}(x)=2 x-\left|x-x^2\right|\) isMHT CET 2025 Medium
- If \(\bar{a}=3 \hat{\imath}+\hat{\jmath}-\hat{k}, \bar{b}=2 \hat{\imath}-\hat{\jmath}+7 \hat{k}\) and \(\bar{c}=7 \hat{\imath}-\hat{\jmath}+23 \hat{k}\) are three vectors,
then which of the following statement is true.MHT CET 2020 Easy - The abscissae of the points of the curve \(\mathrm{y}=x^3\) are in the interval \([-2,2]\), where the slope of the tangents can be obtained by 5. Mean Value Theorem for the interval \([-2,2]\) areMHT CET 2025 Medium
- Let \(O\) be the origin and let \(P Q R\) be an arbitrary triangle. The point \(S\) \(\overline{O P} \cdot \overline{O Q}+\overline{O R} \cdot \overline{O S}=\overline{O R} \cdot \overline{O P}+\overline{O Q} \cdot \overline{O S}=\) \(\overline{O Q} \overline{O Q} \cdot \overline{O R}+\overline{O P} \cdot \overline{O S}\) that \(\overline{O P} \cdot \overline{O Q}+\overline{O R} \cdot \overline{O S}=\overline{O R} \cdot \overline{O P}+\overline{O Q} \cdot \overline{O S}=\) \(\overline{O Q} \cdot \overline{O R}+\overline{O P} \cdot \overline{O S}\), then the triangle \(P Q R\) has \(S\) as itsMHT CET 2022 Medium
- Find \(\frac{d y}{d x}\), if \(x=2 \cos \theta-\cos 2 \theta\) and
\(y=2 \sin \theta-\sin 2 \theta .\)MHT CET 2009 Easy - Let \(f(\theta)=\sin \left(\tan ^{-1}\left(\frac{\sin \theta}{\sqrt{\cos 2 \theta}}\right)\right)\), where \(\frac{-\pi}{4} \lt \theta \lt \frac{\pi}{4}\), then the value of \(\frac{d}{d(\tan \theta)}(f(\theta))\) isMHT CET 2024 Medium
More PYQs from MHT CET
- At thermodynamics process of uncontrolled change satisfying the equation \(Q=W=0\), is \([Q=\) heat supplied, \(W=\) work done \(]\)MHT CET 2022 Easy
- The equations of the lines which make intercepts on the axes whose sum is 8 and
product is 15 areMHT CET 2020 Medium - Calculate the number of moles of nonvolatile solute dissolved in 0.5 kg solvent if molal elevation constant for solvent is \(2 \mathrm{~kg} \mathrm{~K} \mathrm{~mol}^{-1}\) \(\left[\Delta \mathrm{T}_{\mathrm{b}}=0.8 \mathrm{~K}\right]\)MHT CET 2025 Easy
- Struvite stones are derived from _____.MHT CET 2020 Medium
- Which of the following statements is false about oxygen and sulphur?MHT CET 2025 Medium
- Stalk of an anatropous angiosperm ovule is called ________.MHT CET 2025 Medium