Problem 9: Which of the following statements is FALSE for all noncircular ellips

Question

Problem 9: Which of the following statements is FALSE for all noncircular ellipses? (A) The eccentricity, e, is less than one. (B) The ellipse has two foci. (C) The sume of the two distances from the two foci to any point on the ellipse is 2a (i.e., twice the semimajor distance). (D) The coefficients 4 and C prededin g the x2 and y terms in the general form of the equation are equal. Problem 10: The equation y = a, +a2x is an algebraic expression for which of the following? (A) a cosine expansion series (B) projectile motion (C) a circle in polar form (D) a straight line

Explanation / Answer

problem 9

A B and C are true

D is the false statement

general equation of a noncircular ellipse is ax2+2hxy+by2+2gx+2fy+c=0

Coeffients of x2 and y2 are not equal. Since coeffients of x2 and y2 represents lenghts of semi major axis and semi minor axis of the ellipse respectively. If coeffients of x2 and y2 are equal then lenghts of semi major axis and semi minor axis are equal then given ellipse become a circle.

therefor answer is option D

problem 10

answer is option D

y = mx+c is the slope-interceot form of the equation of a straight line.

Thus y = a1+a2x is an algebraic expression of a straight line.  

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