How to find the coordinates?

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How to find the coordinates?

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Answer 1 · 2018-02-25T08:04:05

$(x, y) = (\frac{4}{9}, 2)$ $(x, y)=(4/9, 2)$

Explanation:

$4 y = 9 x + 4$ $4y=9x+4$
$y^{2} = 9 x$ $y^2=9x$
All we need to do is to solve the system of equations, the solutions are the required points, so:
$9 x = 4 y - 4$ $9x=4y-4$
$x = \frac{4 y - 4}{9}$ $x=(4y-4)/9$
$y^{2} = 9 \cdot \frac{4 y - 4}{9}$ $y^2=9*(4y-4)/9$
$y^{2} - 4 y + 4 = 0$ $y^2-4y+4=0$
${(y - 2)}^{2} = 0$ $(y-2)^2=0$
$y = 2$ $y=2$
$x = \frac{4}{9}$ $x=4/9$
thus the required coordinated are:
$(x, y) = (\frac{4}{9}, 2)$ $(x, y)=(4/9, 2)$

Answer 2 · 2018-02-25T08:57:15

$(x, y) \to (\frac{4}{9}, 2)$ $(x,y)to(4/9,2)$

Explanation:

$4 y = 9 x + 4 \to (1)$ $4y=9x+4to(1)$

$y^{2} = 9 x \to (2)$ $y^2=9xto(2)$

$from equation (1) x 9 x = 4 y - 4 \to (3)$ $"from equation "(1)color(white)(x)9x=4y-4to(3)$

$substitute 9 x = 4 y - 4 in equation (2)$ $"substitute "9x=4y-4" in equation "(2)$

$y^{2} = 4 y - 4 \leftarrow rearrange and equate to zero$ $y^2=4y-4larrcolor(blue)"rearrange and equate to zero"$

$\Rightarrow y^{2} - 4 y + 4 = 0$ $rArry^2-4y+4=0$

$\Rightarrow {(y - 2)}^{2} = 0 \Rightarrow y = 2$ $rArr(y-2)^2=0rArry=2$

$substitute y = 2 in equation (3)$ $"substitute "y=2" in equation "(3)$

$9 x = 8 - 4 \Rightarrow x = \frac{4}{9}$ $9x=8-4rArrx=4/9$

$point of contact = (\frac{4}{9}, 2)$ $"point of contact "=(4/9,2)$
graph{(y-9/4x-1)(y^2-9x)=0 [-10, 10, -5, 5]}

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How to find the coordinates?

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