TS EAMCET · Maths · Parabola
The equation of the parabola with focus \((0,0)\) and directrix \(x+y=4\) is
- A \(x^2+y^2-2 x y+8 x+8 y-16=0\)
- B \(x^2+y^2-2 x y+8 x+8 y=0\)
- C \(x^2+y^2+8 x+8 y-16=0\)
- D \(x^2-y^2+8 x+8 y-16=0\)
Answer & Solution
Correct Answer
(A) \(x^2+y^2-2 x y+8 x+8 y-16=0\)
Step-by-step Solution
Detailed explanation
Given focus of parabola is \(S(0,0)\). Equation of directrix is \(x+y=4\) Let \(P(x, y)\) be any point on the parabola. Now, \(S P^2=P M^2\) \(\Rightarrow \quad(x-0)^2+(y-0)^2=\left[\frac{x+y-4}{\sqrt{1+1}}\right]^2\) \(\Rightarrow \quad x^2+y^2=\frac{(x+y-4)^2}{2}\)…
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 normal to a circle \(S=0\) at \(P(1,3)\) is \(x+2 y=7\) and it has another normal at \(Q(3,5)\) which is the polar of the point \(A\left(7,-\frac{1}{2}\right)\) with respect to the circle \(x^2+y^2-4 x+6 y-12=0\). Then, the equation of the circle \(S=0\) isTS EAMCET 2018 Medium
- If \(\tan \alpha=\frac{-12}{5}, \cot \beta=\frac{7}{24}, \alpha\) does not belong to second quadrant and \(\beta\) does not belong to first quadrant, then \(\sqrt{13} \sin \frac{\alpha}{2}+\cos \frac{\beta}{2}+\tan \frac{\alpha}{2} \cot \frac{\beta}{2}=\)TS EAMCET 2023 Easy
- \(\int_0^3\left|x^2-3 x+2\right| d x=\)TS EAMCET 2023 Medium
- If \(a b \neq 0\) and the sum of the coefficients of \(x^7\) and \(x^4\) in the expansion of \(\left(\frac{x^2}{a}-\frac{b}{x}\right)^{11}\) is 0 , thenTS EAMCET 2012 Medium
- Consider the following statements.
a) If a function is differentiable at a point then it is not continuous at
b) If a function is not continuous at then it is not differentiable at
c) If then is not differentiable but continuous on
d) If then
Which of the above statements are (is) correct?TS EAMCET 2021 Easy - If a tangent to the circle \(x^2+y^2+2 x+2 y+1=0\) is radical axis of the circles \(x^2+y^2+2 g x+2 f y+c=0\) and \(2 x^2+2 y^2+3 x+8 y+2 c=0\), thenTS EAMCET 2025 Hard
More PYQs from TS EAMCET
- Helium molecule is two times heavier than hydrogen molecule at \(298 \mathrm{~K}\). According to kinetic theory, the average kinetic energy of helium at \(298 \mathrm{~K}\) isTS EAMCET 2018 Medium
- According to significant figure convention, the result obtained by adding \(12.11,18.0\) and 1.012 isTS EAMCET 2015 Easy
- The product of real of the equation \(|x|^{6 / 5}-26|x|^{3 / 5}-27=0\)TS EAMCET 2012 Medium
- \(\mathrm{CaCO}_3\) reacts with \(\mathrm{HCl}\) to produce \(\mathrm{CaCl}_2, \mathrm{CO}_2\) and \(\mathrm{H}_2 \mathrm{O}\). The approximate mass (in \(\mathrm{g}\) ) of \(\mathrm{CaCO}_3\) \({ }_3\) required to react completely with \(25 \mathrm{~mL}\) of \(0.75 \mathrm{M} \mathrm{HCl}\) is (atomic mass of \(\mathrm{Ca}=40, \mathrm{C}=12\), \(\mathrm{O}=16, \mathrm{Cl}=35.5\) and \(\mathrm{H}=1\) )TS EAMCET 2018 Hard
- The area of cross-section of a potentiometer wire is \(6 \times 10^{-7} \mathrm{~m}^2\). The potential difference per unit length of the potentiometer wire when it is connected to a cell of negligible internal resistance and a resistor in series is \(0.15 \mathrm{Vm}^{-1}\). If the current through potentiometer wire is 0.3 A, then the resistivity of the material of the potentiometer wire isTS EAMCET 2025 Medium
- For \(a \neq b \neq c\), if the lines \(x+2 a y+a=0\), \(x+3 b y+b=0\) and \(x+4 c y+c=0\) are concurrent, then \(a, b, c\) are inTS EAMCET 2018 Easy