Question

The equation of parabola with vertex at origin the axis is along x-axis and passing through the point (2, 3) is​

Answer 1

EXPLANATION.

Equation of parabola with vertex at origin the axis is along the x-axis.

passing through the point = (2,3).

As we know that,

Equation of parabola = y² = 4ax.

Substitute the value of x and y in equation, we get.

⇒ (3)² = 4a(2).

⇒ 9 = 8a.

⇒ a = 9/8.

Substitute this value into main equation, we get.

⇒ y² = 4(9/8)x.

⇒ y² = (9/2)x.

⇒ 2y² = 9x.

                                                                                         

MORE INFORMATION.

Length of intercept.

The length of intercept made by line y = mx + c on the parabola,

y² = 4ax is AB = 4/m² √a(1 + m²)(a - mc).

Conditions of tangency.

(1) = The line y = mx + c touches a parabola y² = 4ax then c = a/m.

(2) = The line y = mx + c touches a parabola x² = 4ay if c = -am².

Equation of tangent.

(1) = Point form = The equation of a tangent to the parabola y² = 4ax at the point (x₁, y₁) is yy₁ = 2a(x + x₁) or T = 0.

(2) = Parametric form = The equation of the tangent to the parabola at t.

that is (at², 2at) is ty = x + at².

(3) = Slope Form = The equation of the tangent of the parabola y² = 4ax is y = mx + a/m.

Answer 2

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${\large{\bold{\rm{\large{Given \; that}}}}}$

★ The axis is along x-axis and passing through the point (2, 3).

${\large{\bold{\rm{\large{To \; determine}}}}}$

★ The equation of parabola with vertex at origin the axis is along x-axis and passing through the point (2, 3) is ?

${\large{\bold{\rm{\large{Solution}}}}}$

★ The equation of parabola with vertex at origin the axis is along x-axis and passing through the point (2, 3) is ${\bold{\red{2y^{2} \: = \: 9x}}}$

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${\large{\bold{\rm{\large{Using \: concept}}}}}$

★ The equation of parabola with vertex at origin the axis is given by what?

${\large{\bold{\rm{\large{Using \: formula}}}}}$

★ The equation of parabola with vertex at origin the axis is given by ${\bold{\red{y^{2} \: = \: 4ax}}}$

${\tt{Here,}}$

$\; \; \; \; \; \;{\bold{\longrightarrow y^{2} \: is \: 3^{2}}}$

$\; \; \; \; \; \;{\bold{\longrightarrow x \: is \: 2}}$

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${\large{\bold{\rm{\large{Full \; Solution}}}}}$

~ Now we have to put the values according to the dimension..!

${\sf{:\implies y^{2} \: = 4ax}}$

${\sf{:\implies 3^{2} \: = 4a(2)}}$

${\sf{:\implies 3 \times 3 \: = 4a(2)}}$

${\sf{:\implies 9 \: = 4a(2)}}$

${\sf{:\implies 9 \: = 8a}}$

${\sf{:\implies 9/8 \: = a}}$

${\sf{:\implies a \: = 9/8}}$

~ Now let's us imply the value of a as 9/8 in that dimension again to get correct and full solution..!

${\sf{:\implies y^{2} \: = 4ax}}$

${\sf{:\implies y^{2} \: = 4(9/8)x}}$

${\sf{:\implies y^{2} \: = (9/2)x}}$

• (× = ÷) ; (÷ = ×)

${\sf{:\implies 2y^{2} \: = 9x}}$

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