Identify the center, foci, vertices and asymptotes then sketch graph of hyperbola

The video tutorial explains how to identify the center and A/B values in standard form equations, focusing on hyperbolas. It distinguishes between hyperbolas and ellipses, emphasizing the importance of the negative sign in hyperbolas. The tutorial guides viewers through sketching hyperbolas, identifying vertices and foci, and graphing asymptotes. It highlights key formulas and provides visual representation tips.

What is the correct way to identify the center of a hyperbola in standard form?

• By using the coordinates directly from the equation

• By swapping the x and y coordinates

• By using the formula X - H, Y - K

• By adding the coefficients of x and y

How do you determine if an equation represents a hyperbola or an ellipse?

• By checking if a^2 is larger than b^2

• By checking if the equation is in standard form

• By looking for a negative sign in the equation

• By comparing the coefficients of x and y

What is the relationship between a^2, b^2, and c^2 in a hyperbola?

• a^2 - b^2 = c^2

• a^2 = b^2 + c^2

• a^2 = b^2 - c^2

• a^2 + b^2 = c^2

Where do the vertices and foci of a hyperbola lie?

• On the x-axis

• On the conjugate axis

• On the transverse axis

• On the y-axis

How can you estimate the position of the foci in a hyperbola?

• By graphing the equation

• By estimating between known square roots

• By using the distance formula

• By calculating the exact decimal value

What is the formula for the asymptotes of a hyperbola with a vertical transverse axis?

• y = ± b/a * (y - k) + h

• y = ± b/a * (x - h) + k

• y = ± a/b * (x - h) + k

• y = ± a/b * (y - k) + h

What is the significance of the slope in the asymptotes of a hyperbola?

• It shows the steepness of the asymptotes

• It indicates the direction of the transverse axis

• It affects the position of the center

• It determines the width of the hyperbola