TS EAMCET · Maths · Circle
A rhombus is inscribed in the region common to the two circles \(x^2+y^2-4 x-12=0\) and \(x^2+y^2+4 x-12=0\). If the line joining the centres of these circles and the common chord of them are the diagonals of this rhombus, then the area (in Sq. units) of the rhombus is
- A \(16 \sqrt{3}\)
- B \(4 \sqrt{3}\)
- C \(12 \sqrt{3}\)
- D \(8 \sqrt{3}\)
Answer & Solution
Correct Answer
(D) \(8 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
The circles have centers \((2,0)\) and \((-2,0)\) and radius is 4 \(\therefore y\)-axis is their common chord. \(\triangle \mathrm{ABC}\) is equilateral \(\Delta\). Hence, area of \(A D B C=\frac{2 \times \sqrt{3}}{4}(4)^2=8 \sqrt{3}\)
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
- For the parabola \(y=\frac{h^3}{3} x^2+\frac{h^2}{2} x-h+\frac{3}{4 h^3}\) if the equation of directrix is \(y=k\), then \(k: h\)TS EAMCET 2020 Hard
- If one of the lines in the pair of straight line given by \(4 x^2+6 x y+k y^2=0\) bisects the angle between the coordinate axes, then \(k \in\)TS EAMCET 2011 Medium
- If \(\cot \theta=-\frac{2}{3}\) and \(\theta\) does not lie in the \(4^{\text {th }}\) quadrant, then \(\frac{(5 \sin \theta+\cos \theta)^2}{\tan \theta+\cot \theta}=\)TS EAMCET 2023 Easy
- \((a, b)\) is the point to which the origin has to be shifted by translation of axes so as to remove the first-degree terms from the equation \(2 x^2-3 x y+4 y^2+5 y-6=0\). If the angle by which the axes are to be rotated in positive direction about the origin to remove the \(x y\)-term from the equation \(a x^2+23 a b x y+b y^2=0\) is \(\theta\), then \(\tan 2 \theta=\)TS EAMCET 2024 Medium
- If \(5 x-12 y+10=0\) and \(12 y-5 x+16=0\) are two tangents to a circle, then the radius of the circle isTS EAMCET 2003 Easy
- \(\int_{-2}^2|[x]| d x\) is equal toTS EAMCET 2003 Hard
More PYQs from TS EAMCET
- Let be the set of all real numbers. Statement I : The function defined by is a one - one function. Statement II : The function defined by is a one-one function. Which of the above statements is(are) true?TS EAMCET 2022 Medium
- Which of the following is the strongest reducing agent?TS EAMCET 2023 Easy
- If \(\alpha, \beta, \gamma\) are the roots of \(x^3+4 x+1=0\), then the equation whose roots are \(\frac{\alpha^2}{\beta+\gamma}, \frac{\beta^2}{\gamma+\alpha}\), \(\frac{\gamma^2}{\alpha+\beta}\) isTS EAMCET 2009 Medium
- If the ratio of the mass numbers of two nuclei is \(27: 125\), then the ratio of their surface areas isTS EAMCET 2025 Medium
- The velocity of a particle having magnitude of \(10 \mathrm{~ms}^{-1}\) in the direction of \(60^{\circ}\) with positive \(\mathrm{X}\)-axis isTS EAMCET 2023 Medium
- The decreasing order of stability of the given carbocations is:
TS EAMCET 2021 Medium