Question

The number of parabolas passing through the three points $(1,3),(6,13),(-5,-9)$ is

• A. $3$
• B. $2$
• C. $0$
• D. infinite

Answer 1

The correct option is C $0$

Suppose a parabola passes through the given three points $(1,3),(6,13),(-5,-9)$

General equation of parabola is: $y=a{x}^2+bx+c$

Since, the above three points passes through parabola, therefore they must satisfy the general equation of parabola.

Substituting them we get:

$3=a+b+c$

$13=36a+6b+c$

$-9=25a-5b+c$

Solving them we get solution as:

$a=0,b=2,c=1$

Thus the equation of parabola that passes through all the three points must be:

$y=\left(0\right)x^2+2x+\left(1\right)$

i.e., $y=2x+1$

which is not a parabola.

Thus, there is no parabola that passes through the points $(1,3),(6,13),(-5,-9)$