AP EAMCET · Maths · Ellipse
The equation of a common tangent to the circle \(x^2+y^2=16\) and to the ellipse \(\frac{x^2}{49}+\frac{y^2}{4}=1\) is
- A \(y=x+\sqrt{45}\)
- B \(y=x+\sqrt{53}\)
- C \(\sqrt{11} y=2 x+4\)
- D \(\sqrt{11} y=2 x+4 \sqrt{15}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{11} y=2 x+4 \sqrt{15}\)
Step-by-step Solution
Detailed explanation
\(c^2 = 16(1+m^2)\) \(c^2 = 49m^2+4\) \(16(1+m^2) = 49m^2+4\) \(16+16m^2 = 49m^2+4\) \(33m^2 = 12 \implies m^2 = \frac{4}{11}\) \(m = \pm \frac{2}{\sqrt{11}}\) \(c^2 = 16(1+\frac{4}{11}) = 16(\frac{15}{11})\) \(c = \pm \frac{4\sqrt{15}}{\sqrt{11}}\)…
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
- A line \(L\) has intercepts \(a\) and \(b\) on the coordinate axes. When the axes are rotated through a given angle \(\theta\) keeping the origin fixed, this line \(L\) has the intercepts \(p\) and \(q\). ThenAP EAMCET 2019 Medium
- If \(\bar{a}=\bar{i}+\bar{j}, \bar{b}=2 \bar{j}-\bar{k}\) are two vectors such that \(\bar{r} \times \bar{a}=\bar{b} \times \bar{a}, \bar{r} \times \bar{b}=\bar{a} \times \bar{b}\), then the unit vector in the direction of \(\overline{\mathrm{r}}\) isAP EAMCET 2025 Medium
- If \((3,-1)\) is one end of a diameter of the circle \(x^2+y^2-2 x+4 y=0\), then the equation of the tangent at the other end of that diameter isAP EAMCET 2017 Hard
- The number of natural numbers less than 1000 , in which no two digits are repeated, is :AP EAMCET 2006 Medium
- Find the particular solution of the following differential equation, given that \(y=1\), when \(x=0,\left(1+x^2\right) \frac{d y}{d x}=e^{m\left(\tan ^{-1} x\right)}-y\)AP EAMCET 2021 Medium
- In \(\triangle A B C,(a+b+c)\left(\tan \frac{A}{2}+\tan \frac{B}{2}\right)\) is equal toAP EAMCET 2007 Medium
More PYQs from AP EAMCET
- \([1+\sec 2 \theta][1+\sec 4 \theta]=\)AP EAMCET 2023 Easy
- If the height of a projectile at a time of 2 s from the beginning of motion is 60 m, then the time of flight of the projectile is (Acceleration due to gravity \(=10 \mathrm{~m} \mathrm{~s}^{-2}\) )AP EAMCET 2025 Medium
- The mass numbers of two elements \(X\) and \(Z\) are 52 and 75 respectively. \(X\) contains \(16.6 \%\) more neutrons compared to protons. \(Z\) contains \(27.3 \%\) more neutrons compared to protons. \(X\) and \(Z\) are respectivelyAP EAMCET 2018 Medium
- The plane passing through \((2,1,-3)\) and perpendicular to \(3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) contains the pointsAP EAMCET 2021 Medium
- A non-conducting body floats in a liquid at \(20^{\circ} \mathrm{C}\) with \(\frac{2}{3}\) of its volume immersed in the liquid. When liquid temperature is increased to \(100^{\circ} \mathrm{C}, \frac{3}{4}\) of body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of container of the liquid)AP EAMCET 2011 Medium
- Four digit numbers with all digits distinct are formed using the digits \(1,2,3,4,5,6,7\) in all possible ways. If \(p\) is the total number of numbers thus formed and \(q\) is the number of numbers greater than 3400 among them, then \(p: q=\)AP EAMCET 2024 Easy