MHT CET · Maths · Parabola
The cartesian co-ordinates of the point on the parabola \(y^{2}=x\) whose parameter is \(\frac{-4}{3}\) are
- A \(\left(\frac{4}{9}, \frac{4}{3}\right)\)
- B \(\left(\frac{4}{3}, \frac{-4}{3}\right)\)
- C \(\left(\frac{4}{3}, \frac{4}{9}\right)\)
- D \(\left(\frac{4}{9}, \frac{-2}{3}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{4}{9}, \frac{-2}{3}\right)\)
Step-by-step Solution
Detailed explanation
\(y^{2}=x \quad t=-4 / 3\)
\(a=\frac{1}{4}\)
\(\left(a t^{2}, 2 a t\right)\)
\(=\left(\frac{1}{4} \cdot \frac{16}{9} 4, \frac{-2}{3}\right)=\left(\frac{4}{9}, \frac{-2}{3}\right)\)
\(a=\frac{1}{4}\)
\(\left(a t^{2}, 2 a t\right)\)
\(=\left(\frac{1}{4} \cdot \frac{16}{9} 4, \frac{-2}{3}\right)=\left(\frac{4}{9}, \frac{-2}{3}\right)\)
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 Rolle's theorem holds for the function \(\mathrm{f}(x)=x^3+\mathrm{b} x^2+\mathrm{ax}+5\) on \([1,3]\) with \(\mathrm{c}=2+\frac{1}{\sqrt{3}}\), then the values of \(a\) and \(b\) respectively areMHT CET 2024 Easy
- If \(y=\tan ^{-1}\left(\frac{4 \sin 2 x}{\cos 2 x-6 \sin ^2 x}\right)\), then \(\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)\) at \(x=0\) isMHT CET 2023 Hard
- If the vectors \(\vec{a}=2 \hat{i}+p \hat{j}+4 \hat{k}\) and \(\vec{b}=6 \hat{i}-9 \hat{j}+q \hat{k}\) are collinear, then \(\mathrm{p}\) and \(\mathrm{q}\) areMHT CET 2021 Easy
- The population of a town increases at a rate proportional to the population at that time. If the population increases from forty thousand to eighty thousand in 20 years, then the population in another 40 years will beMHT CET 2025 Medium
- \(\mathrm{f}: \mathbb{R}-\left(-\frac{3}{5}\right) \rightarrow \mathbb{R}\) is defined by \(f(x)=\frac{3 x-2}{5 x+3}\), then \(f \circ f(1)\) isMHT CET 2023 Easy
- Dual of \(\left(x^{\prime} \vee y^{\prime}\right)=x \wedge y\) isMHT CET 2008 Medium
More PYQs from MHT CET
- The value of \(a\), so that the volume of parallelepiped formed by \(\hat{i}+a \hat{j}+\hat{k}, \hat{j}+a \hat{k}\) and \(a \hat{i}+\hat{k}\) becomes minimum isMHT CET 2022 Easy
- In a step-down transformer, the number of turns inMHT CET 2012 Easy
- The value of \(\frac{(\cos \theta+i \sin \theta)^4}{(\sin \theta+i \cos \theta)^5}=\) where \(i=\sqrt{-1}\)MHT CET 2025 Medium
- For \(x \in R, f(x)=|\log 2-\sin x|\) and \(g(x)=f(f(x))\), thenMHT CET 2022 Hard
- The value of \(\lim _{x \rightarrow 0} \frac{x}{|x|+x^2}\) is .MHT CET 2024 Easy
- What is numerical value of rate constant of a first order reaction that is \(20 \%\) completed in 10 minute ?MHT CET 2025 Medium