If a parabola having its axis parallel to the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Since the axis of the parabola is parallel to the $X$-axis,the equation of the parabola is of the form $x = ay^2 + by + c$  $(i)$.Given that the p

Vedclass · Accepted Answer

$\left(\frac{5}{2}, 0\right)$

Vedclass · Answer

(A) Since the axis of the parabola is parallel to the $X$-axis,the equation of the parabola is of the form $x = ay^2 + by + c$  $(i)$.Given that the points $(0, -1)$,$(6, 1)$,and $(-2, -3)$ lie on the parabola,we have:$0 = a - b + c$  $(ii)$$6 = a + b + c$  $(iii)$$-2 = 9a - 3b + c$  $(iv)$Subtracting $(ii)$ from $(iii)$,we get $2b = 6$,so $b = 3$.Substituting $b = 3$ into $(ii)$ and $(iii)$,we get $a + c = 3$ and $a + c = 3$ (consistent).Substituting $b = 3$ into $(iv)$,we get $-2 = 9a - 9 + c$,so $9a + c = 7$.Solving $a + c = 3$ and $9a + c = 7$,we subtract the first from the second to get $8a = 4$,so $a = \frac{1}{2}$.Then $c = 3 - \frac{1}{2} = \frac{5}{2}$.The equation is $x = \frac{1}{2}y^2 + 3y + \frac{5}{2}$.To find the point where it cuts the $X$-axis,set $y = 0$:$x = \frac{1}{2}(0)^2 + 3(0) + \frac{5}{2} = \frac{5}{2}$.Thus,the point is $\left(\frac{5}{2}, 0\right)$.

If a parabola having its axis parallel to the $X$-axis passes through the points $(0, -1)$,$(6, 1)$,and $(-2, -3)$,then the point at which this parabola cuts the $X$-axis is

Similar Questions

The equation of the tangent at $P(-4, -4)$ on the curve $x^{2} = -4y$ is

If the normal to the parabola $y^2 = 4ax$ intersects the axis of the parabola at a distance of $4a$ from the vertex,then the slopes of the normal are in which progression?

If the line $y = 2x + k$ is a normal to the parabola $y^2 = 4x$ at the point $(t^2, 2t)$,then:

The equations $x = \frac{t}{4}$ and $y = \frac{t^2}{4}$ represent:

If the focal chord drawn through the point $P(5,5)$ to the parabola $y^2=5x$ meets the parabola again at the point $Q$,then the tangent drawn to this parabola at $Q$ meets the axis of the parabola at the point

Vedclass Test Series

Exam Paper Generator

Online Exam Module