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Find the length of the chord made by 3x2 - y2 = 3 and y + x – 5 = 0.

User Acalypso
by
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1 Answer

5 votes

Answer:

The correct answer is "9√2 units".

Explanation:

The given equations are:


3x^2-y^2=3...(equation 1)


y+x-5=0...(equation 2)

According to the 2nd equation, we get


y+x-5=0


y=5-x

On substituting the value of "y" in the 1st equation, we get


3x^2-y^2=3


3x^2-(5-x)^2=3


3x^2-(25+x^2-10x)=3


2x^2+10x-28=0

On taking common, we get


x^2+5x-14=0

On applying factorization, we get


x^2+7x-2x-14=0


x(x+7)-2(x+7)=0


(x+7)(x-2)=0


x+7=0


x=-7

or,


x-2=0


x=2

Now,

The points are:

(-7, 12) = (x₁, y₁)

(2, 3) = (x₂, y₂)

By using the distance formula, the length of chord will be:

=
√((x_2-x_1)^2+(y_2-y_1)^2)

On substituting the values in the above formula, we get

=
√((2-(-7))^2+(3-12)^2)

=
√((9)^2+(-9)^2)

=
√(81+81)

=
9 √(2) units

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