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Question Number 31846 by momo last updated on 15/Mar/18

25[(x−2)^2 +(y−3)^2 ]=(3x−4y+7)^2   is the equation of parabola.Find  length of latus rectum

$$\mathrm{25}\left[\left({x}−\mathrm{2}\right)^{\mathrm{2}} +\left({y}−\mathrm{3}\right)^{\mathrm{2}} \right]=\left(\mathrm{3}{x}−\mathrm{4}{y}+\mathrm{7}\right)^{\mathrm{2}} \\ $$$${is}\:{the}\:{equation}\:{of}\:{parabola}.{Find} \\ $$$${length}\:{of}\:{latus}\:{rectum} \\ $$

Commented by momo last updated on 16/Mar/18

how

$${how} \\ $$

Commented by momo last updated on 16/Mar/18

explain with sol^n

$${explain}\:{with}\:{sol}^{{n}} \\ $$

Answered by Tinkutara last updated on 16/Mar/18

(x−2)^2 +(y−3)^2 =(((3x−4y+7)/5))^2   (√((x−2)^2 +(y−3)^2 ))=∣((3x−4y+7)/5)∣  Focus=(2,3)  Directrix is 3x−4y+7=0  Distance of focus from directrix=2a  2a=∣((6−12+7)/5)∣=(1/5)  4a=(2/5)

$$\left({x}−\mathrm{2}\right)^{\mathrm{2}} +\left({y}−\mathrm{3}\right)^{\mathrm{2}} =\left(\frac{\mathrm{3}{x}−\mathrm{4}{y}+\mathrm{7}}{\mathrm{5}}\right)^{\mathrm{2}} \\ $$$$\sqrt{\left({x}−\mathrm{2}\right)^{\mathrm{2}} +\left({y}−\mathrm{3}\right)^{\mathrm{2}} }=\mid\frac{\mathrm{3}{x}−\mathrm{4}{y}+\mathrm{7}}{\mathrm{5}}\mid \\ $$$${Focus}=\left(\mathrm{2},\mathrm{3}\right) \\ $$$${Directrix}\:{is}\:\mathrm{3}{x}−\mathrm{4}{y}+\mathrm{7}=\mathrm{0} \\ $$$${Distance}\:{of}\:{focus}\:{from}\:{directrix}=\mathrm{2}{a} \\ $$$$\mathrm{2}{a}=\mid\frac{\mathrm{6}−\mathrm{12}+\mathrm{7}}{\mathrm{5}}\mid=\frac{\mathrm{1}}{\mathrm{5}} \\ $$$$\mathrm{4}{a}=\frac{\mathrm{2}}{\mathrm{5}} \\ $$

Commented by momo last updated on 16/Mar/18

thanks sir

$${thanks}\:{sir} \\ $$

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