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NDA Math Conic Section

Consider the following for the next two (02) items that follow:

Consider the parabola

y=x^{2}+7x+2

and the straight line

y=3x-3

[NDA II 2016]

Question : 25 of 34

Marks: +1, -0

Solution:

Parabola Equation:

y=x^{2}+7x+2

Line equation:

y=3x-3

Since all the points given in the options lie on the parabola

Thus we will calculate the distance from the given line to these points:

for

(0,2)

: distance

=\;\;\frac{\left|3(0)-(2)-3\right|}{\sqrt{(3)^{2}+(-1)^{2}}}=\;\;\frac{5}{\sqrt{10}}

for

(-2,-8)

: distance

=\;\;\frac{\left|3(-2)-(-8)-3\right|}{\sqrt{10}}=\;\;\frac{1}{\sqrt{10}}

for

(-7,2)

: distance

=\;\;\frac{\left|3(-7)-2-3\right|}{\sqrt{10}}=\;\;\frac{26}{\sqrt{10}}

for

(1,10)

: distance

=\;\;\frac{\left|3(1)-10-3\right|}{\sqrt{10}}=\;\;\frac{10}{\sqrt{10}}

\therefore (-2,-8)

is the given point.

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