TS EAMCET · Maths · Parabola
If the tangent drawn at the point \(P(4,8)\) to the parabola \(y^2=16 x\) meets the parabola \(y^2=16 x+80\) at \(A\) and \(B\), then the mid-point of \(A B\) is
- A \((9,6)\)
- B \((4,8)\)
- C \((4,1)\)
- D \((2,3)\)
Answer & Solution
Correct Answer
(B) \((4,8)\)
Step-by-step Solution
Detailed explanation
Equation of tangent to the parabola \(y^2=16 x\) at point \(P(4,8)\) is \(8 y=8(x+4) \Rightarrow y=x+4\) \(\ldots(\mathrm{i})\) \(\because\) Tangent (i) meets the another parabola \(y^2=16 x+80\) at \(A\) and \(B\), so on solving them we have \((x+4)^2=16 x+80\)…
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 \(f(x)=\frac{1}{1+\frac{1}{x}}\) and \(g(x)=\frac{1}{1+\frac{1}{f(x)}}\), then \(g^{\prime}(2)\) is equal toTS EAMCET 2013 Easy
- \(\lim _{n \rightarrow \infty} \frac{(2 n(2 n-1) \ldots(n+2)(n+1))^{1 / n}}{n}=\)TS EAMCET 2025 Hard
- The incentre of the triangle formed by the straight line having as -intercept and as -intercept, together with the coordinate axes, isTS EAMCET 2018 Easy
- If \(f(x)=\frac{x\left(a^x-1\right)}{1-\cos x}\) and \(g(x)=\frac{x\left(1-a^x\right)}{a^x\left(\sqrt{1-x^2}-\sqrt{1+x^2}\right)}\), then \(\lim _{x \rightarrow 0}(f(x)-g(x))=\)TS EAMCET 2025 Hard
- If \(\alpha, \beta, \gamma\) are the roots of the equation \(5 x^3-3 x^2+2 x-4\) \(=0\) then \(\sum \alpha^2 \beta^2=\).TS EAMCET 2022 Easy
- For the coefficient of inTS EAMCET 2021 Medium
More PYQs from TS EAMCET
- The system of equations \(4 x+y+2 z=5\), \(x-5 y+3 z=10,9 x-3 y+7 z=20\) hasTS EAMCET 2015 Medium
- If the slope of the tangent drawn at any point \((x, y)\) on the curve \(y=f(x)\) is \(\left(6 x^2+10 x-9\right)\) and \(f(2)=0\), then \(f(-2)=\)TS EAMCET 2024 Easy
- The area of the region bounded by the curves \(x=y^2-2\) and \(x=y\) isTS EAMCET 2017 Medium
- The equation of the straight line passing through the point \((3,2)\) and inclined at angle of \(60^{\circ}\) with the line \(\sqrt{3} x+y=1\) isTS EAMCET 2023 Medium
- In which of the following reactions at equilibria, the position of the equilibrium shifts towards the products, if the total pressure is increased? (i) \(\mathrm{X}_2(\mathrm{~g})+3 \mathrm{Y}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{XY}_3(\mathrm{~g})\) (ii) \(\mathrm{X}_2(\mathrm{~g})+\mathrm{Y}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{XY}(\mathrm{g})\) (iii) \(\mathrm{X}_2(\mathrm{~g})+\mathrm{Z}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{XZ}(\mathrm{g})\) (iv) \(\mathrm{X}_2(\mathrm{~g})+\mathrm{Y}_4(\mathrm{~g}) \rightleftharpoons 2 \mathrm{XY}_2(\mathrm{~g})\)TS EAMCET 2022 Easy
- The order of reactivity of phenol (I), nitrobenzene (II) and benzene (III) towards nitration isTS EAMCET 2011 Easy