AP EAMCET · Maths · Circle
Let \(\theta\) be the angle between the circles \(S \equiv x^2+y^2+2 x-2 y+c=0\) and \(S^1 \equiv x^2+y^2-6 x-8 y+9=0\). If \(c\) is an integer and \(\cos \theta=\frac{5}{16}\) then the radius of the circle \(\mathrm{S}=0\) is
- A 2
- B 4
- C 3
- D 1
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
\(C_1=(-1,1)\), \(r_1=\sqrt{1^2+(-1)^2-c}=\sqrt{2-c}\) \(C_2=(3,4)\), \(r_2=\sqrt{(-3)^2+(-4)^2-9}=\sqrt{16}=4\) \(d=\sqrt{(3-(-1))^2+(4-1)^2}=\sqrt{4^2+3^2}=\sqrt{25}=5\) \(\cos \theta = \frac{d^2 - r_1^2 - r_2^2}{2 r_1 r_2}\)…
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
- Bag \(B_1\) contains 4 white and 2 black balls. Bag \(B_2\) contains 3 white and 4 black balls. A bag is chosen at random and a ball is drawn from it at random, then the probability that the ball drawn is white, isAP EAMCET 2023 Hard
- The equation of the hyperbola with focus \((1,2), e=\sqrt{3}\) and directrix \(2 x+y=1\) is given byAP EAMCET 2020 Hard
- If each of the observations \(x_1, x_2, \ldots, x_n\) is increased or decreased by \(k\), where \(k\) is a positive number, then the variance of the daAP EAMCET 2023 Easy
- Let \(\mathrm{e}\) be the eccentricity of the ellipse \(\frac{\mathrm{x}^2}{4}+\frac{\mathrm{y}^2}{9}=1\). If \(\frac{1}{\mathrm{e}}\) is the eccentricity of a hyperbola, then the eccentricity of its conjugate hyperbola isAP EAMCET 2023 Medium
- If , thenAP EAMCET 2019 Easy
- The mean and variance of a binomial variable are and respectively. The probability that takes values greater than , isAP EAMCET 2021 Medium
More PYQs from AP EAMCET
- At , saturated solution of was found to have a specific conductivity of and that of water being used is . If the ionic conductance's of and are and respectively, the solubility of at will be [Atomic masses ofAP EAMCET 2021 Medium
- \(\sum_{k=1}^6\left[\sin \frac{2 k \pi}{7}-i \cos \frac{2 k \pi}{7}\right]\) is equal toAP EAMCET 2015 Medium
- A magnet of magnetic moment \(M\) is rotated through \(360^{\circ}\) in a magnetic field \(H\), the work done will beAP EAMCET 2020 Easy
- \(\lim _{x \rightarrow-\infty} \frac{5 x^3-x^2 \sin 5 x}{x \cos 4 x+7|x|^3-4|x|+3}=\)AP EAMCET 2025 Medium
- Assertion (A) Finely divided charcoal can act as an adsorbent.
Reason (R) Finely divided material has small surface area.AP EAMCET 2022 Easy - A diffraction pattern is obtained by using a beam of red light. If the red light is replaced by the blue lightAP EAMCET 2023 Medium