AP EAMCET · Maths · Straight Lines
The midpoint of the diagonal of a rectangle formed by \(x^2+5 x-6=0\) and \(y^2-8 y-20=0\) is
- A \(\left(\frac{5}{2}, 4\right)\)
- B \(\left(\frac{-5}{2},-6\right)\)
- C \(\left(\frac{-5}{2}, 4\right)\)
- D \(\left(\frac{5}{2},-6\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{-5}{2}, 4\right)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \mathrm{x}^2+5 \mathrm{x}-6=0 \Rightarrow \mathrm{x}^2+6 \mathrm{x}-\mathrm{x}-6=0 \\ & \Rightarrow(\mathrm{x}-1)(\mathrm{x}+6)=0 \Rightarrow \mathrm{x}_1, \mathrm{x}_2=1,-6 \\ & \mathrm{y}^2-8 \mathrm{y}-20=0 \Rightarrow \mathrm{y}^2-10 \mathrm{y}+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
- Find the equation of a straight line passing through and cutting off equal intercepts on the co-ordinate axes.AP EAMCET 2021 Easy
- The direction cosines of the line which is perpendicular to the lines with direction cosines proportional to \(\langle 1,-2,-2\rangle\) and \(\langle 0,2,1\rangle\) is given byAP EAMCET 2020 Easy
- If the line \(2 b x+3 c y+4 d=0\) passes through the points of intersection of \(y^2=4 a x\) and \(x^2=4 a y\), thenAP EAMCET 2021 Hard
- A circle cuts off positive intercepts 5 and 6 on the \(x\) and \(y\) axes respectively, and passes through the origin. Then the equation of the circle isAP EAMCET 2020 Medium
- The value of \(\lambda\) with \(|\lambda| < 16\) such that \(2 x^2-10 x y+12 y^2+5 x+\lambda y-3=0\) represents a pair of straight lines, isAP EAMCET 2009 Medium
- If \(\int(1-\cos x) \operatorname{cosec}^2 x d x=f(x)+c\), then \(f(x)\) is equal toAP EAMCET 2010 Medium
More PYQs from AP EAMCET
- Which one of the following is a semiconductor?AP EAMCET 2023 Easy
- A ball of mass \(2 \mathrm{~g}\) moving with a velocity of \(2 \mathrm{~ms}^{-1}\) collides with another ball of mass \(8 \mathrm{~g}\) which is at rest and comes to rest after collission. Then the coefficient of restitution isAP EAMCET 2017 Easy
- The condition that the roots of \(x^3-b x^2+c x-d=0\) are in geometric progression isAP EAMCET 2010 Easy
- An electrostatic paint sprayer has a metal sphere of diameter \(18 \mathrm{~cm}\) and at a potential of \(25 \mathrm{kV}\). The charge on the metal sphere isAP EAMCET 2017 Easy
- The angle between lines represented by \(\left(\sin ^2 \alpha\right) y^2-2 x y\left(\cos ^2 \alpha\right)+\left(\cos ^2 \alpha-1\right) x^2=0\) isAP EAMCET 2021 Easy
- Two sources \(A\) and \(B\) are sending notes of frequency \(680 \mathrm{~Hz}\). A listener moves from \(A\) and \(B\) with a constant velocity \(u\). If the speed of sound in air is \(340 \mathrm{~ms}^{-1}\), what must be the value of \(u\) so that he hears 10 beats per second?AP EAMCET 2009 Easy