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2 years ago

I WILL GIVE BRAINLY

Mathematics

1 answer:

Gnom [1K]2 years ago

3 0

9514 1404 393

Answer:

m^2 = 35/9

Step-by-step explanation:

The line will be tangent to the ellipse where there is one point of intersection between the line and the ellipse. We can find that case by looking at the discriminant of the quadratic.

x^2 +9(mx +2)^2 = 1

x^2 +9(m^2x^2 +4mx +4) = 1

(9m^2 +1)x^2+36mx +35 = 0 . . . . subtract 1, collect terms

Then the discriminant is ...

(36m)^2 -4(9m^2 +1)(35)

We want it to be zero, so we have ...

1296m^2 -1260m^2 -140 = 0 . . . . eliminate parentheses

36m^2 = 140 . . . . . . . . . . . . . . . add 140

m^2 = 140/36 . . . . . . . . . . . . divide by 36

m^2 = 35/9

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BabaBlast [244]

$\underline{\bf{Given \:equation:-}}$

$\\ \sf{:}\dashrightarrow ax^2+by+c=0$

$\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.$

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$\boxed{\sf \sqrt{\sqrt{a}}=a}$

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$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}$

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$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}$

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$\underline{\bf More\: simplification:-}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}$

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$\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}$

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elena-14-01-66 [18.8K]

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Total number of participants= 276

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Answer:

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