Equation of an ellipse
→having center (0,0) , vertex (
and covertex
and focus
is given by:

As definition of an ellipse is that locus of all the points in a plane such that it's distance from two fixed points called focii remains constant.
Consider two points (a,0) and (-a,0) on Horizontal axis of an ellipse:
Distance from (a,0) to (c,0) is = a-c = 
Distance from (-a,0) to (c,0) is = a + c = 
a -c + a +c
= a + a
= 2 a →(Option A )
Answer:
x = -1.59
Step-by-step explanation:
We are here given a equation and we need to solve out for x. The given equation is ,
Take log to the base " e " on both sides , so that we can remove the variable from the exponent .

Simplify using the property of log ,
, we have ,
Distribute by opening the brackets ,
This can be written as ,
Divide both sides by ln 4 ,
Simplify ,
On simplifying , we will get ,
Answer: x = 2.65, y = 3.81
Step-by-step explanation:
ABC similar to PQR
1) Find the ratio of corresponding sides
2) Use that ratio to find values for x & y
1) Side AB = 2.76cm & Side PR = <em>y</em><em> </em>cm
Side BC = <em>x</em> cm & Side RQ = 3.66 cm
Side CA = 3 cm & Side QP = 4.14 cm (both lengths given)
Can match 3 to 4.14 & ratio of sides in ABC to PQR= 3 /4.14
Length of sides ABC = 3/4.14 times the length of sides PQR
2) x = (3 / 4.14) * 3.66 = 2.65
Now solve for y, ABC to PQR: 2.76 = (3 / 4.14) (<em>y </em>)
<em>equality property</em> (both sides) & inverse operation to isolate <em>y : </em> . 2.76 ÷ (3 / 4.14) = (3 / 4.14 ) ÷ (3 / 4.14) (<em>y</em><em>)</em>
2.76 * (4.14 / 3) = 3 / 4.14 * (4.14 / 3) (<em>y</em><em>)</em>
(2.76 * 1.38 ) = 3.81 = <em>y</em>
<em></em>
<em>Scale Factor Method: Determine the Multiplier</em>
Small to Big or Big to Small ➜ Be sure not to switch
<em>Directed numbers</em> are numbers that have either a <u>positive</u> or <u>negative </u>sign, which can be shown on a <em>number line</em>. Therefore, point F is Fifteen-halves of line <em>segment</em> DE.
A <u>number line</u> is a system that can show the positions of <em>positive</em> or <em>negative</em> numbers. It has its <em>ends</em> ranging from <em>negative infinity</em> to <em>positive infinity</em>. Thus any <em>directed</em> number can be located on the line.
Directed numbers are numbers with either a <u>negative</u> or <u>positive </u>sign, which shows their direction with respect to the <em>number line.</em>
In the given question, the <u>distance</u> between points D and E is <em>9 units</em>. So that <em>dividing</em> 9 units in the ratio of 5 to 6, we have;
x 9 = 
= 
Therefore, the <em>location</em> of point F, which <u>partitions</u> the directed line segment from d to E into a 5:6 ratio is
. Thus the<em> answer</em> is <u>Fifteen-halves.</u>
For further clarifications on a number line, visit: brainly.com/question/23379455
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