TS EAMCET · Maths · Pair of Lines
If the line \(2 x+b y+5=0\) forms an equilateral triangle with \(a x^2-96 b x y+k y^2=0\), then \(a+3 k=\)
- A \(3 b\)
- B 192
- C \(4 b^2\)
- D 102
Answer & Solution
Correct Answer
(B) 192
Step-by-step Solution
Detailed explanation
We know that pair of lines \(\left(a^2-3 b^2\right) x^2+8 a b x y+\left(b^2-3 a^2\right) y^2=0\) with the lines \(a x+b y+c=0\) forms an equilateral triangle. So, put \(a=2, c=5\) \(\left(4-3 b^2\right) x^2+16 b x y+\left(b^2-12\right) y^2=0\)...(i) Given pair of lines :…
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
- Match the items of List-I with those of List-II
Then, which of the following is correct?
TS EAMCET 2018 Medium - Let be any point on the circle and be its centre. Let be the chord of contact of with respect to the circle . Then the locus of the circumcentre of the triangle isTS EAMCET 2022 Medium
- The equation of a line making an angle \(60^{\circ}\) with the line \(x+y-3=0\) and passing through the point \((1,1)\) isTS EAMCET 2020 Easy
- In a \(\triangle A B C\), if \(\tan A: \tan B: \tan C=1: 2: 3\) and \(\sin A: \sin B: \sin C=\sqrt{5}: 2 \sqrt{2}: k\), then \(k=\)TS EAMCET 2020 Medium
- If \(f(x)=\left|\begin{array}{ccc}x & x+1 & x+3 \\ x+2 & x+4 & x+7 \\ x+6 & x+9 & x+13\end{array}\right|\), then \(f(5)=\)TS EAMCET 2022 Easy
- When \(a\) is irrational, the number of solutions satisfying the equation \(1+\sin ^2 a x=\cos x\) isTS EAMCET 2018 Easy
More PYQs from TS EAMCET
- \(\begin{aligned} & \text { If } \int x^4(\log x)^3 d x=x^5\left[A(\log x)^3+B(\log x)^2+C \log x+D\right] \ & +k, \text { then } A+B+C+5 D=\end{aligned}\)TS EAMCET 2023 Medium
- In a triangle \(\mathrm{ABC}\), if \(\mathrm{r}_1=2 \mathrm{r}_2=3 \mathrm{r}_3\), then \(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}=\)TS EAMCET 2023 Hard
- If \(f(x)=\sqrt{\operatorname{Cos}^{-1} \sqrt{1-x^2}}\), then \(f^{\prime}\left(\frac{1}{2}\right)=\)TS EAMCET 2025 Medium
- Product of reaction between Aluminium with aqueousTS EAMCET 2022 Medium
- If \((2,-1,3)\) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane isTS EAMCET 2023 Medium
- The centroid of the triangle formed by the pair of straight lines \(12 x^2-20 x y+7 y^2=0\) and the line \(2 x-3 y+4=0\) is :TS EAMCET 2006 Easy