JEE Mains · Maths · STD 11 - 9. straight line
Suppose that the points \((h, k), (1, 2)\) and \((-3, 4)\) lie on the line \(L_1\). If a line \(L_2\) passing through the points \((h, k)\) and \((4, 3)\) is perpendicular to \(L_1\), then \(\frac{k}{h}\) equals
- A \(-\frac{1}{7}\)
- B \(\frac{1}{3}\)
- C \(3\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
equation of \({L_1}\) is \(x + 2y = 5\) and equation or \({L_2}\) is \(2x - y = 5\) Their point of intersection is \((3,1)\) \( \Rightarrow \frac{k}{h} = \frac{1}{3}\)
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 \(f: R \rightarrow R\) is given by \(f(x)=x+1\), then the value of \(\lim _{n \rightarrow \infty} \frac{1}{n}\left[f(0)+f\left(\frac{5}{n}\right)+f\left(\frac{10}{n}\right)+\ldots+f\left(\frac{5(n-1)}{n}\right)\right]\), is:JEE Mains 2021 Hard
- A circle passing through the point \(P (\alpha, \beta)\) in the first quadrant touches the two coordinate axes at the points \(A\) and \(B\). The point \(P\) is above the line \(A B\). The point \(Q\) on the line segment \(A B\) is the foot of perpendicular from \(P\) on \(A B\). If \(P Q\) is equal to \(11\) units, then the value of \(\alpha \beta\) is \(.............\).JEE Mains 2023 Hard
- Let \(z = 1 + ai\) be a complex number, \(a > 0\), such that \(z^3\) is areal number. Then the sum \(1 + z + z^2 + .... + z^{11}\) is equal toJEE Mains 2016 Hard
- Let the set of all positive values of \(\lambda\), for which the point of local minimum of the function \(\left(1+x\left(\lambda^2-x^2\right)\right)\) satisfies \(\frac{x^2+x+2}{x^2+5 x+6}<0\), be \((\alpha, \beta)\). Then \(\alpha^2+\beta^2\) is equal to ...........JEE Mains 2024 Hard
- Let \(x=x(y)\) be the solution of the differential equation \(2 y \,e^{x / y^{2}} d x+\left(y^{2}-4 x e^{x / y^{2}}\right) d y=0\) such that \(x(1)=0\). Then, \(x(e)\) is equal toJEE Mains 2022 Hard
- Let the equation \(x^{2}+y^{2}+p x+(1-p) y+5=0\) represent circles of varying radius \(\mathrm{r} \in(0,5]\). Then the number of elements in the set \(S=\left\{q: q=p^{2}\right.\) and \(\mathrm{q}\) is an integer \(\}\) is ..... .JEE Mains 2021 Hard
More PYQs from JEE Mains
- From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is :JEE Mains 2026 Easy
- If \(\sum_{ k =1}^{10} K ^{2}\left(10_{ C _{ K }}\right)^{2}=22000 L\), then \(L\) is equal to \(.....\)JEE Mains 2022 Hard
- The number of distinct solutions of the equation \(\log _{\frac{1}{2}}|\sin x|=2-\log _{\frac{1}{2}}|\cos x|\) in the interval \([0,2 \pi],\) isJEE Mains 2020 Hard
- If the equation, \(x^{2}+b x+45=0(b \in R)\) has conjugate complex roots and they satisfy \(|z+1|=2 \sqrt{10},\) thenJEE Mains 2020 Hard
- \(\lim\limits_{x \rightarrow 0}\left(\frac{3 x^{2}+2}{7 x^{2}+2}\right)^{\frac{1}{x^{2}}}\) is equal toJEE Mains 2020 Hard
- The total number of \(3-digit\) numbers, whose sum of digits is \(10,\) isJEE Mains 2020 Hard