Problem 15 Easy Difficulty

Find the equations of the hyperbola satisfying the given conditions.
Foci $(0, \pm \sqrt{10})$, passing through $(2,3)$

Answer

$\frac{y^2}{5} - \frac{x^2}{5}=1$

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Precalculus

NCERT Class 11 - Math

Chapter 11

Conic Sections

Section 4

Parabola

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Problem 15

Video Transcript

in this problem, we first observed that the folk I, which is zero comma plus minus route then is only by access, which means that the equation of the Ebola is of the form. Why square by square minus X squared by b squared equals to one. Mhm. Now, since the focus on the FOCA is at zero comma plus minus routine means that C equals two, wrote them. Now, since it passes through the point or two comma three, substitute. This is 9:00 air squared minus. This is two squared is four divided by B squared equals to what we know from here. That C square is nothing but a squared plus B square or 10 equals to a squared plus b square, which means that be square is nothing. But then minus is square. So let's substitute it here. This is 9. 9 is square minus four upon then minus is square equals to one. Now let's take the L c M. This is is square then minuses squared. This is 90 nine. A square minus four. Air square equal storm. So we get 90 minus 13. You square it will stop many square minus a power for it's just nothing but a powerful -23. A Square plus 90 equals two. Z. Now this can be written us, You buy four 18 a square minus five ways square plus 90 equals to zero. Continue here. This is is square, you square minus 18 minus five. He Square -18 equals to zero. So we get e squared minus five into a Square -18 equals to zero. So we have it can take any positive values. So we have a as Route five or Route 80. Now we know that in the happy Ebola she is greater than a so it cannot be rotating. So the only possible value of is look fine which means that be square is nothing, but then minus eight square inches 10 minus five which is fine. Now let's get the equation of the hip Ebola. My substituting in me this is why square by square is five minus Extra. Square by B. Square is also five is equals two. What? This is the question. That's.

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