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Find an equation for the conic that satisfies the given conditions: hyperbola, vertices (-2, -4), (-2, 6), foci (-2, -5), (-2, 7)...

Question

Find an equation for the conic that satisfies the given conditions: hyperbola, vertices (-2, -4), (-2, 6), foci (-2, -5), (-2, 7)

Find an equation for the conic that satisfies the given conditions: hyperbola, vertices (-2, -4), (-2, 6), foci (-2, -5), (-2, 7)



Answers

Find an equation for the conic that satisfies the given conditions.

Hyperbola, vertices $ (-1, 2) $, $ (7, 2) $, foci $ (-2, 2) $, $ (8, 2) $

Hey, it's clear. So inhuman right here. So we're gonna use the definition of hyperbole using silicon, which is the absolute value of P f sub one minus the absolute value of P of sub too is equal to plus or minus square plus or minus two A. So we know that the distance between the two Verte sees is 10. So he sucks the two ton when we get square root of X plus three square plus why plus seven square minus square room of X plus three square was why minus nine square is equal to plus or minus 10. We're gonna move the plus or minus 10 so we get square room X plus three square less lie plus seven square is equal to plus or minus 10 last square room X plus three square plus one minus nine split square. Both sides X plus three square plus why plus seven square is equal to 10 square. It's less explicit. Three square plus Why minus nine square plus or minus 20 square root X plus three square plus Why minus nine square We get why plus seven square minus y minus nine square minus 100 as equal to plus or minus 20 square root of X plus three square plus Why minus nine. Then we got to. Why minus two on 16 minus 100. It's equal to plus or minus 20 square root. X plus three square plus Why minus nine. Square me. Why minus minus 25 is equal to plus or minus by square room of X plus three square plus y minus nine square. Then we get eight. Why minus 33 is equal to plus or minus five square room x plus three square plus Why minus nine square square both sides When we got speak. Why minus 33 square is equal to 25. That's plus three. Square was 25. Why minus nine square? Don't we get eight wine minus 33 square minus five Y minus 45 square is equal to 25 times X plus three square. Don't we get 64? Why square minus 16 times 33. Why most 33 square minus 25 watt square minus or 150. Why less 45 I swear, was equal to 25 times that sex less three square, which gives us 39 why square minus 70 feet. Why minus 930 six is equal to 25 tons X plus three square. Then we get 39. Why square minus two? Why? Plus one minus one minus 939. Sequel to 25 times X plus three square, which gives us 39 times why minus one square minus 25 times. Next plus three square is equal to 975 We get why minus one square over 25 minus X plus three square over 39. Yes, he looked to one.

Hey, it's Claire is the one you read here. So hyper below the equation is life square over a square, minus X square over. Being square is equal to one you have. Verdecia is of zero comma, plus or minus two in the full guy. Zero comma, plus or minus Fine. He is equal to this sea is equal to mine. Two chocolate Be swear you five square is equal to two square plus B square. So be square is equal to 21. The equation we get becomes why square over four minus X square over 21 is equal to one.

And this problem we wish to find the equation for the Given Connick hyperbole with vertex is negative 12 and 72 and focus on the negative 22 and eight. To this question is challenge your understanding of how to identify the equation for a comic given its parameters to solve. Remember that hyper politics one of two forms we can utilize the form of are given verticals and folks to determine which form it is because only the X values of our furnaces and folks are changing. We must have enough hyperbole to form one H plus or minus a h plus or minus act. That's from Form one. We extract from this information that K is two, Y is three, A is four and 80 S five. The four is taken from the vertex is change from the um center point and the A is taken from the pro side. Change. Thus for agent K given we have that be as route 80 square minutes A squared equals three. Yeah. Thus we have the final form of recreation given here note that Are y equals three. Here actually corresponds to art h value rather than why value. Hence we end up with the final equation X minus three squared over 16 plus one minus two square over nine equals one.

Hey, is there a sizzling you read here? So we have the folk I to be plus or a minus two comma zero the vergis ese her plus or minus five comma. Zero. So the centre is between the vergis ese. So has to be zero comma. Zero. We get a to be equal to five and see to be equal to. So be square is equal to 25 miss four, which is equal to 21. So we're going to plug it into the lips equation. So we get X minus zero square over five square plus my minus dura square over 21 was equal to one. This gives us X square over 25 lost. Why? Square over 21 is equal to one.


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