Question

Equation of the parabola whose axis is horizontal and passing through the points $\left(-2,1\right),\left(1,2\right),\left(-1,3\right)$ is

Answer 1

Equation of Parabola with horizontal axis $x=a{y}^2+by+c...\left(1\right)$

Since points $(-2,1),(1,2),(-1,3)$ passes through parabola, so they satisfy equation (1) and we have,

$-2=a+b+c...\left(2\right)$

$1=4a+2b+c...\left(3\right)$
$-1=9a+3b+c...\left(4\right)$

Solving equation 2,3 and 4 we get $a=\frac{-5}{2},b=\frac{21}{2},c=-10$

Thus equation of parabola is $x=\left(\frac{-5}{2}\right)y^2+\left(\frac{21}{2}\right)y-10\Rightarrow 5y^2+2x-21y+20=0$