A hyperbola has vertices (5,0) and (-5,0). Its
1 answer:
Answer:
The equation of the hyperbola
Step-by-step explanation:
Given hyperbola vertices are (5,0) and (-5,0)
The foci of the hyperbola is (61,0) and (- 61,0) so the foci is lie on x-axis
here the vertex a =5 and foci ('c')= 61
we know the condition
now substitute a =5 and c= 61
b^2 = 61^2 - 5^2 = 3696
a^2 = 25
The equation of the hyperbola
The equation of the hyperbola
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Answer:
∠EGB and ∠AGF are congruent;
Transitive Property of Equality
Step-by-step explanation:
The vertical angles theorem is about the angles that are opposite to each other. These angles are formed when two lines cross each other
Vertical angles are congruent i.e their measures are equal
Look at the attached graph
Given:
AB // CD
E , G , H , F are col-linear
The line which contains points E , G , H , F is a transversal for the parallel lines AB and CD
∵ AB and EF intersected at point G
∴ m∠EGB = m∠AGF ⇒ by the vertical angles theorem
When lines AB and EF intersected at G they formed opposite angles like angles EGB and AGF, then angles EGB and AGF are congruent ( vertical angle theorem)
∵ AB // CD and EF is a transversal
∴ m∠AGF = m∠CHF (corresponding angles theorem)
Transitive Property of Equality: if one angle is equal to two other angles, then the two other angles are equal
Therefore, If a = b and b = c, then a = c
∵ m∠EGB = m∠AGF
∵ m∠AGF = m∠CHF
∴ m∠EGB = m∠CHF (transitive property theorem)
∠EGB and ∠AGF are congruent; Transitive Property of Equality
