Question

en connect Enhanced MATH Question 14 of 14 (1 point) Attempt 1 of Unlimited Write the standard form of an equation of an ellipse subject to the given conditions. Vertices: (4.5) and (4, 5); Foc: (4, V10) and (4. 10). The equation of the ellipse in standard form is Save For Later Check Answer Mewton Algher

please help me work this out. thank you very much.

Answer 1

The ginfoi thre ellipse Theiven Veitices ellipse Heste, 4, VIo) and (4VID) Ven Csle aie ,5) and (4,-5 10m the 5 and - 5) tre 7i ven veahices 2-Coordinates asle A ad doiom the i ven foci vio) and Vio the n-Co ordtinates ate 4 The x Co oYdinates of the vesitices and foci ale the same axis is pata llel to the axis majon Thus, ihe equation of the ellipse will have the fooim: So, the |(x-A) whele, .) is the centre of the ellipse dength of majoo eneth of minor axis a is ha ofthe axis halp of the stepl: Sdertily The cente is the midpoint the vetices the centei , ) t. ) and 2, . y) the fosmula omidpoint is

the iven vea ticrs Midpoin centeo (4, 5) and (4,-5) (A, is (44 55 The cente ,4)- 4,0 ind a value step2: The ength the majos axis is 2a we solve to a by findng the dis tance between the -co ordinates ef the vestices 2a +5- -5) 55 a a . 25 Stepa: ind c hese, foci toi aie , VID) and 4,VID aste Ven tc th 4,0 K= O

vertex 4,5 focus4,vio Minor ais 2 Centen (4,0) (A,k) Majo OP Axis touy4VID) (h, -c) 2a Vesiter l4,5)

Step 4: ind ae have ushede, lo and a-a5 2. 25-b Substihuting these values in the stardand equation 2 -A) 2 h,k 4,0) 25 5 2 (4 25 15 (2- is the standasid fosm zuation f given etlepse S