AP EAMCET · Maths · Pair of Lines
If one of the lines represented by \(a x^2+2 h x y+b y^2=0\) bisects the angle between the positive coordinate axes, then
- A \(a+b=2 h\)
- B \(a-b=2 h\)
- C \(a+2 h+b=0\)
- D \(a+2 h-b=0\)
Answer & Solution
Correct Answer
(C) \(a+2 h+b=0\)
Step-by-step Solution
Detailed explanation
The line bisecting the angle between the positive coordinate axes is \(y=x\). Substitute \(y=x\) into \(a x^2+2 h x y+b y^2=0\): \(a x^2+2 h x (x)+b (x)^2=0\) \(a x^2+2 h x^2+b x^2=0\) \(x^2(a+2 h+b)=0\) \(a+2 h+b=0\)
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 equation of a normal to the circle \(x^2+y^2-2 x=0\) that is parallel to the line \(x+2 y-\) \(3=0\) isAP EAMCET 2020 Medium
- The line \(x=\frac{\pi}{4}\) divides the area of the region bounded by \(y=\sin x, y=\cos x\) and \(x\)-axis \(\left(0 \leq x \leq \frac{\pi}{2}\right)\) into two regions of areas \(A_1\) and \(A_2\). Then \(A_1, A_2\) equalsAP EAMCET 2009 Medium
- If \(x \sqrt{1+y}+y \sqrt{1+x}=0\), then \(\frac{d y}{d x}\) is equal toAP EAMCET 2005 Medium
- In any triangle \(\mathrm{ABC}, a(b \cos C-c \cos B)=\)AP EAMCET 2022 Hard
- When two dice are thrown, the probability of getting the sum of the values on them as 10 or 11 isAP EAMCET 2024 Easy
- \(\mathrm{P}, \mathrm{Q}\) and R try to hit the same target one after the other. If their probabilities of hitting the target are \(\frac{2}{3}, \frac{3}{5}, \frac{5}{7}\) respectively, then the probability that the target is hit by P or Q but not by R isAP EAMCET 2024 Easy
More PYQs from AP EAMCET
- Identify the correct statement(s) from the following
a) Dipole moment of \(\mathrm{NH}_3\) is more than \(\mathrm{NF}_3\)
b) \(\mathrm{SF}_4\) is square planar
c) \(\mathrm{SnCl}_4\) is more covalent than \(\mathrm{SnCl}_2\)
d) \(\mathrm{In}_2 \mathrm{SO}_4\) sulphur atom has expanded octetAP EAMCET 2017 Easy - If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3-6 x^2+11 x-6=0\) and if \(a=\alpha^2+\beta^2+\gamma^2\), \(b=\alpha \beta+\beta \gamma+\gamma \alpha\) and \(c=(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)\), then the correct inequality among the following isAP EAMCET 2010 Hard
- The descending order of magnitude of the eccentricities of the following hyperbolas is
A. A hyperbola whose distance between foci is three times the distance between its directrices.
B. Hyperbola in which the transverse axis is twice the conjugate axis.
C. Hyperbola with asymptotes
\(x+y+1=0, x-y+3=0\)AP EAMCET 2024 Easy - Find the solution of differential equation given below:AP EAMCET 2020 Hard
- The polynomial equation of degree 5 whose roots are the roots of the equation \(x^5-3 x^4-x^3+11 x^2-12 x+4=0\) each increased by 2, isAP EAMCET 2025 Medium
- If \(y=\sqrt{x+\sqrt{x+\sqrt{x+\ldots \ldots \infty}}}\), then \(\frac{d y}{d x}\) is equal toAP EAMCET 2021 Medium