$$Statement-1$$: If the foci of a hyperbola are at the points (4$$, $$1) and $$($$–$$6$$, $$1)$$, eccentricity is $$5/4$$ then the length of the transverse axis is $$8$$.$$Statement-2$$: Distance between the foci of a hyper bola is equal to the product of its eccentricity and the length of the transverse axis

Question

$$Statement-1$$: If the foci of a hyperbola are at the  points (4$$, $$1) and $$($$–$$6$$, $$1)$$, eccentricity is $$5/4$$ then the length of the transverse axis is $$8$$.$$Statement-2$$: Distance between the foci of a hyper bola is equal to the product of its eccentricity and the length of the transverse axis

Infinity Learn · Accepted Answer

$$Statement-2$$ is true, as the distance between the foci of $$x2a2$$−$$y2b2=1$$ is $$2ae$$ where $$2a$$ is the length of the transverse axis and e is the eccentricityUsing it in $$statement-1$$, length of the transverse axis  is $$(4+6)25/4=10$$×$$45=8$$ and thus $$statement-1$$ is also true.

Statement-1: If the foci of a hyperbola are at the points (4, 1) and (–6, 1), eccentricity is 5/4 then the length of the transverse axis is 8.
Statement-2: Distance between the foci of a hyper bola is equal to the product of its eccentricity and the length of the transverse axis

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Statement-1: If the foci of a hyperbola are at the points (4, 1) and (–6, 1), eccentricity is 5/4 then the length of the transverse axis is 8.Statement-2: Distance between the foci of a hyper bola is equal to the product of its eccentricity and the length of the transverse axis

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Statement-1: If the foci of a hyperbola are at the points (4, 1) and (–6, 1), eccentricity is 5/4 then the length of the transverse axis is 8.
Statement-2: Distance between the foci of a hyper bola is equal to the product of its eccentricity and the length of the transverse axis