enEnglishguગુજરાતી
JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Statement \(-1:\) The line \(x - 2y = 2\) meets the parabola, \(y^2 + 2x = 0\) only at the point \((-2, - 2).\) Statement \(-2:\) The line \(y = mx - \frac{1}{{2m}}(m \ne 0)\) is tangent to the parabola, \(y^2 = - 2x\) at the point \(\left( { - \frac{1}{{2{m^2}}}, - \frac{1}{m}} \right).\)
- A Statement \(-1\) is true; Statement \(-2\) is false.
- B Statement \(-1\) is true; Statement \(-2\) is true; Statement \(-2\) is a correct explanation for statement \(-1.\)
- C Statement \(- 1\) is false; Statement \(-2\) is true.
- D Statement \(-1\) a true; Statement \(-2\) is true; Statement \(-2\) is not a correct explanation for statement \(-1.\)
Answer & Solution
Correct Answer
(B) Statement \(-1\) is true; Statement \(-2\) is true; Statement \(-2\) is a correct explanation for statement \(-1.\)
Step-by-step Solution
Detailed explanation
Both satements are true and satement-\(2\) is the correct expalnation of satement-\(1\) \(\therefore \) The straight line \(y = mx + \frac{a}{m}\) is always a tangent to the parabola \({y^2} = 4ax\) for any value of \(m\). The co-ordinates of point of contact…
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 the plane passing through the point \((-1,0,-2)\) and perpendicular to each of the planes \(2 x+y-\) \(z=2\) and \(x-y-z=3\) be \(a x+b y+c z+8=0\). then the value of \(a+b+c\) is equal to:JEE Mains 2021 Medium
- Equation of a plane at a distance \(\sqrt{\frac{2}{21}}\) from the origin, which contains the line of intersection of the planes \(x-y-z-1=0\) and \(2 x+y-3 z+4=0\) is :JEE Mains 2021 Hard
- Let \({ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}-1}=28,{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=56\) and \({ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}+1}=70\). Let \(\mathrm{A}(4 \cos t, 4 \sin t), \mathrm{B}(2 \sin t,-2 \cos \mathrm{t})\) and \(C\left(3 r-n, r^2-n-1\right)\) be the vertices of a triangle \(A B C\), where \(t\) is a parameter. If \((3 x-1)^2+(3 y)^2\) \(=\alpha\), is the locus of the centroid of triangle ABC , then \(\alpha\) equalsJEE Mains 2025 Hard
- Let \(A\) be a point on the line \(\vec r = \left( {1 - 3\mu } \right)\hat i + \left( {\mu - 1} \right)\hat j + \left( {2 + 5\mu } \right)\hat k\) and \(B(3, 2, 6)\) be a point in the space. Then the value of \(\mu \) for which the vector \(\overrightarrow {AB} \) is parallel to the plane \(x -4y +3z = 1\) isJEE Mains 2019 Hard
- Considering only the principal values of the inverse trigonometric functions, the domain of the function \(f(x)=\cos ^{-1}\left(\frac{x^{2}-4 x+2}{x^{2}+3}\right)\) is.JEE Mains 2022 Medium
- Let \(M\) and \(N\) be the number of points on the curve \(y^{5}-9 x y+2 x=0\), where the tangents to the curve are parallel to \(x\)-axis and \(y\)-axis, respectively. Then the value of \(M + N\) equals \(......\)JEE Mains 2022 Hard
More PYQs from JEE Mains
- The number of seven-digit numbers, that can be formed by using the digits \(1, 2, 3, 5\) and \(7\) such that each digit is used at least once, is :JEE Mains 2026 Hard
- A possible value of \(\tan \left(\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}\right)\) is :JEE Mains 2021 Medium
- Let \(\quad \overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+\alpha \hat{\mathrm{j}}+\hat{\mathrm{k}}, \quad \overrightarrow{\mathrm{b}}=-\hat{\mathrm{i}}+\hat{\mathrm{k}}, \quad \overrightarrow{\mathrm{c}}=\beta \hat{\mathrm{j}}-\hat{\mathrm{k}}\), where \(\alpha\) and \(\beta\) are integers and \(\alpha \beta=-6\). Let the values of the ordered pair \((\alpha, \beta)\) for which the area of the parallelogram of diagonals \(\vec{a}+\vec{b}\) and \(\vec{b}+\vec{c}\) is \(\frac{\sqrt{21}}{2}\), be \(\left(\alpha_1, \beta_1\right)\) and \(\left(\alpha_2, \beta_2\right)\). Then \(\alpha_1^2+\beta_1^2-\alpha_2 \beta_2\) is equal toJEE Mains 2024 Hard
- A straight line \(L\) at a distance of \(4\) units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of \(60^o\) with the line \(x + y = 0\). Then an equation of the line \(L\) isJEE Mains 2019 Hard
- If \(y = {\rm{sec}}\left( {{{\tan }^{ - 1}}x} \right)\) then \(\frac{{dy}}{{dx}}\) at \(x = 1\) is equal to :JEE Mains 2013 Medium
- The image of the point \((3,5)\) in the line \(x-y+1=0\), lies onJEE Mains 2021 Medium