The points which represents the vertices of the given equation are; (15, −2) and (−1, −2).
<h3>Which points among the answer choices represents the vertices of the ellipse whose equation is given?</h3>
The complete question gives the equation of the ellipse as; (x-7)²/64+(y+2)²/9=1.
Since, It follows from convention that general equation of ellipse with centre as (h, k) takes the form;
(x-h)²/a² +(y-k)²/b² = 1.
Consequently, it follows from observation that the value of a and b in the given equation in the task content is; √64 = 8 and √9 = 3 respectively.
Since, 8 > 3, The vertices of the ellipse are given by; (h±a, k).
The vertices in this scenario are therefore;
(7+8, -2) and (7-8, -2).
= (15, -2) and (-1, -2).
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Answer:
1) AD=BC(corresponding parts of congruent triangles)
2)The value of x and y are 65 ° and 77.5° respectively
Step-by-step explanation:
1)
Given : AD||BC
AC bisects BD
So, AE=EC and BE=ED
We need to prove AD = BC
In ΔAED and ΔBEC
AE=EC (Given)
( Vertically opposite angles)
BE=ED (Given)
So, ΔAED ≅ ΔBEC (By SAS)
So, AD=BC(corresponding parts of congruent triangles)
Hence Proved
2)
Refer the attached figure
In ΔDBC
BC=DC (Given)
So,(Opposite angles of equal sides are equal)
So,
So, (Angle sum property)
x+x+50=180
2x+50=180
2x=130
x=65
So,
Now,
So,
In ΔABD
AB = BD (Given)
So,(Opposite angles of equal sides are equal)
So,
So,(Angle Sum property)
y+y+25=180
2y=180-25
2y=155
y=77.5
So, The value of x and y are 65 ° and 77.5° respectively
Given:
In triangle ABC, .
To find:
The angle of depression from point A to point C.
Solution:
According to angle sum property, the sum of all interior angles of a triangle is 180 degrees.
In triangle ABC,
We know that if a transversal line intersect the two parallel lines, then alternate interior angles are equal. So, the angle of depression from point A to point C is equal to the measure of angle C in triangle ABC.
Therefore, the angle of depression is 24 degrees.