TS EAMCET · Maths · Parabola
The length of the latusrectum of the conic \(25\left[(x-2)^2+(y-3)^2\right]=(3 x-4 y+7)^2\) is
- A \(\frac{1}{5}\)
- B \(\frac{2}{5}\)
- C \(\frac{3}{5}\)
- D \(\frac{4}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{2}{5}\)
Step-by-step Solution
Detailed explanation
Given, 25[(x-2) \(\left.)^2+(y-3)^2\right]=[3 x-4 y+7]^2\) is \[ \Rightarrow(x-2)^2+(y-3)^2=\left(\frac{3 x-4 y+7}{\sqrt{25}}\right)^2 \] Its focus \(\equiv(2,3)\), Directrix \(\rightarrow 3 x-4 y+7\) \(\therefore L=\) length of latus rectum \(=2\) (distance between focus and…
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
- The solution of the differential equation \((2 x-3 y+5) d x+(9 y-6 x-7) d y=0\), isTS EAMCET 2019 Medium
- For an ellipse with eccentricity \(\frac{1}{2}\) the centre is at the origin. If one directrix is \(x=4\), then the equation of the ellipse isTS EAMCET 2008 Easy
- If the conjugate of \((x+i y)(1-2 i)\) is \((1+i)\), thenTS EAMCET 2017 Easy
- If \(f(x)=\left|\begin{array}{ccc}x^3+x & x+1 & x-2 \\ 2 x^3+3 x-1 & 3 x & 3 x-3 \\ x^3+2 x+3 & 2 x-1 & 2 x-1\end{array}\right|\), then \(\frac{d}{d x}(f(x))\) is equal toTS EAMCET 2021 Medium
- If \(\alpha\) represents the number of arrangements of \(p\) men and \(q\) women in a row such that all men are together and \(\beta\) represents the number of circular arrangements of the same people with the same condition, then \(\alpha: \beta\) isTS EAMCET 2020 Easy
- If \([x]\) denotes the greatest integer not exceeding \(x\) and if the function \(f\) defined by \(f(x)= \begin{cases}\frac{a+2 \cos x}{x^2} & , x < 0 \ b \tan \frac{\pi}{[x+4]} & , x \geq 0\end{cases}\) is continuous at \(x=0\), then the ordered pair \((a, b)\) is equal toTS EAMCET 2011 Hard
More PYQs from TS EAMCET
- Identify and respectively, in the following reaction sequence are
TS EAMCET 2021 Hard - Which of the following is not the common component of photochemical smog?TS EAMCET 2025 Easy
- Let the escape speed of an object on the earth's surface be \(V_0\). The object is projected out with speed \(5 V_0\). The speed of the object far away from the earth will beTS EAMCET 2022 Easy
- The structure of PCC isTS EAMCET 2013 Hard
- Each of the two orthogonal circles \(C_1\) and \(C_2\) passes through both the points \((2,0)\) and \((-2,0)\). If \(y=m x+c\) is a common tangent to these circles, thenTS EAMCET 2019 Hard
- If a plane electromagnetic wave has electric field oscillations of frequency \(3 \mathrm{GHz}\) then the wavelength of the wave is (speed of light in vacuum \(=3 \times 10^8 \mathrm{~ms}^{-1}\) )TS EAMCET 2023 Hard