MCQ
Let $A(–1, 1)$ and $B(2, 3)$ be two points and $P$ be a variable point above the line $AB$ such that the area of $\Delta PAB$ is $10.$ If the locus of $P$ is $ax + by = 15,$ then $5a + 2b$ is :
- A$-\frac{12}{5}$
- B$-\frac{6}{5}$
- C4
- D6
✓
Answer
$\frac{1}{2}\left|\begin{array}{ccc}h & k & 1 \\ -1 & 1 & 1 \\ 2 & 3 & 1\end{array}\right|=10 $
$ -2 x+3 y=25 $
$ -\frac{6}{5} x+\frac{9}{5} y=15 $
$a=-\frac{6}{5}, b=\frac{9}{5} $
$5 a=-6,2 b=\frac{18}{5}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Let $e_{1}$ and $e_{2}$ be the eccentricities of the ellipse, $\frac{x^{2}}{25}+\frac{y^{2}}{b^{2}}=1(b<5)$ and the hyperbola $\frac{ x ^{2}}{16}-\frac{ y ^{2}}{ b ^{2}}=1$ respectively satisfying $e _{1} e _{2}=1 .$ If $\alpha$ and $\beta$ are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair $(\alpha, \beta)$ is equal to
→The graph of $y = f(x)$ is shown then number of solutions of the equation $f(f(x)) =2$ is
→${\sin ^{ - 1}}\left( {\frac{3}{5}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right) = $
→A straight line $L$ passing through the point $(2,3)$ bounds minimum area with the curve $f (x) = x^2 - 4x + 6$ , then equation of tangent to the Curve parallel to $L$ is
→For $a, b > 0,$ let
→$\int_{}^{} {\frac{{{x^2} - 1}}{{{x^4} + {x^2} + 1}}\;dx = } $
→Suppose that a function $f: R \rightarrow R$ satisfies $f(x+y)=f(x) f(y)$ for all $x, y \in R$ and $f(1)=3 .$ If $\sum \limits_{i=1}^{n} f(i)=363,$ then $n$ is equal to
→If$\frac{{2x}}{{2{x^2} + 5x + 2}} > \frac{1}{{x + 1}}$, then
→Identify the correct statement
→where $[.]$ & $\{.\}$ denotes greatest integer function and fractional part function respectively.
The graph of $y = ax^2 + bx + c$ is shown. Which of the following does $NOT$ hold good?
→