enEnglishguગુજરાતી
JEE Mains · Maths · STD 11 - 9. straight line
If the \(x-\) intercept of some line \(L\) is double as that of the line, \(3x + 4y = 12\) and the \(y-\) intercept of \(L\) is half as that of the same line, then the slope of \(L\) is
- A \(-3\)
- B \(-3/8\)
- C \(-3/2\)
- D \(-3/16\)
Answer & Solution
Correct Answer
(D) \(-3/16\)
Step-by-step Solution
Detailed explanation
Given line \(3x+4y=12\) can be rewritten as \(\frac{{3x}}{{12}} + \frac{{4y}}{{12}} = 1 \Rightarrow \frac{x}{4} + \frac{y}{3} = 1\) \( \Rightarrow \) \(x\) -intercept \(=4\) and \(y\)-intercept \(=3\) Let the required line be \(L:\frac{x}{a} + \frac{y}{b} = 1\) where \(a=x\)…
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
- Let \(\alpha=\frac{-1+i\sqrt{3}}{2}\) and \(\beta=\frac{-1-i\sqrt{3}}{2}\),\(i=\sqrt{-1}\). If \((7-7\alpha+9\beta)^{20}+(9+7\alpha-7\beta)^{20}+(-7+9\alpha+7\beta)^{20}+(14+7\alpha+7\beta)^{20}=m^{10}\) then m is ___ .JEE Mains 2026 Easy
- The total number or irrational terms in the binomial expansion of \(\left( {{7^{1/5}} - {3^{1/10}}} \right)^{60}\) isJEE Mains 2019 Hard
- Given two independent events, if the probability that exactly one of them occurs is \(\frac {26}{49}\) and the probability that none of them occurs is \(\frac {15}{49}\) , then the probability of more probable of the two events isJEE Mains 2013 Hard
- A light ray emits from the origin making an angle \(30^{\circ}\) with the positive \(x\)-axis. After getting reflected by the line \(x + y =1\), if this ray intersects \(x\)-axis at \(Q\), then the abscissa of \(Q\) isJEE Mains 2023 Hard
- \(ABCD \) is a trapezium such that \(AB\) and \(CD \) are parallel and \(BC\; \bot CD\). If \(\angle ADB = \theta \),\(BC=p\) and \( CD=q\) , then \(AB\) is equal to:JEE Mains 2013 Hard
- Let \(a_1 , a_2, a_3, .... , a_n\), be in \(A.P\). If \(a_3 + a_7 + a_{11} + a_{15} = 72\) , then the sum of its first \(17\) terms is equal toJEE Mains 2016 Hard
More PYQs from JEE Mains
- Let C be the circle \(\mathrm{x}^2+(\mathrm{y}-1)^2=2, \mathrm{E}_1\) and \(\mathrm{E}_2\) be two ellipses whose centres lie at the origin and major axes lie on x -axis and y -axis respectively. Let the straight line \(x+y=3\) touch the curves \(C\), \(E_1\) and \(E_2\) at \(P\left(x_1, y_1\right), Q\left(x_2, y_2\right)\) and \(R\left(x_3, y_3\right)\) respectively. Given that \(P\) is the mid-point of the line segment \(Q R\) and \(P Q=\frac{2 \sqrt{2}}{3}\), the value of \(9\left(x_1 y_1+x_2 y_2+x_3 y_3\right)\) is equal to ______ .JEE Mains 2025 Hard
- Let \(\mathrm{a}=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) and \(\beta=\min _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) If \(8 x^{2}+b x+c=0\) is a quadratic equation whose roots are \(\alpha^{1 / 5}\) and \(\beta^{1 / 5}\), then the value of \(c-b\) is equal to:JEE Mains 2021 Hard
- Let the image of the point \(P (1,2,3)\) in the line \(L : \frac{ x -6}{3}=\frac{ y -1}{2}=\frac{ z -2}{3}\) be \(Q .\) let \(R (\alpha, \beta, \gamma)\) be a point that divides internally the line segment \(PQ\) in the ratio \(1: 3\). Then the value of \(22(\alpha+\beta+\gamma)\) is equal toJEE Mains 2022 Hard
- Let \( y=y(x) \) be the solution curve of the differential equation \( (1+x^{2})dy+(y-\tan^{-1}x)dx=0, \) \( y(0)=1 \). Then the value of \( y(1) \) is:JEE Mains 2026 Medium
- Let the circle \(S: 36 x^{2}+36 y^{2}-108 x+120 y+C=0\) be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, \(x-2 y=4\) and \(2 x-y=5\) lies inside the circle \(S\), then :JEE Mains 2021 Hard
- For \(0<\theta<\pi / 2\), if the eccentricity of the hyperbola \(\mathrm{x}^2-\mathrm{y}^2 \operatorname{cosec}^2 \theta=5\) is \(\sqrt{7}\) times eccentricity of the ellipse \(x^2 \operatorname{cosec}^2 \theta+y^2=5\), then the value of \(\theta\) is :JEE Mains 2024 Medium