online algebra 2 test

An ellipse can also be defined as the locus of a point that moves in such a way that the sum of its distances from two fixed points (called foci) is constant . Equation of an ellipse in standard form [x 2 /a 2 ]+[y 2 /b 2 ]=1 Let x'ox and yoy' b..

Let P(x1,y1)be any point on an ellipse (x 2 /a 2 )+(y 2 /b 2 ) = 1 And let Q(x1,y2) be its corresponding point on auxiliary circle (x 2 /a 2 )+(y 2 /a 2 ) = 1 Then (x1 2 /a 2 )+(y1 h..

Proof : - Let P(x1,y1)be any point on an ellipse (x 2 /a 2 )+(y 2 /b 2 ) = 1 And let Q(x1,y2) be its corresponding point on auxiliary circle (x 2 /a 2 )+(y 2 /a 2 ) = 1 Then (x1 2 /a 2 )+(y..

Equations of condition - Study the following equations: a) 4x + 2 = 14 b) x - 7 = 5 - 2x c) 3a - 8 = a + 12 The equation 4x + 2 = 14 is true only when x = 3, Similarly, x - 7 = 5 - 2x is true only when x = 4, and 3a - 8 = a + 23 is true only when a = 10. The ..

Question: Use a graph paper for this question. Draw the graphs of 2x-y-1 = 0 and 2x + y = 9 on the same axes. Use 2cm = 1unit on both the axes and plot only three points per line. Write down the co-ordinates of the point of intersection of the two lines...

- Let e be the eccentricity of an ellipse whose focus is F(p,q) and the equation of whose directrix is ax+by+c=0 Let P(x,y) be a point on the ellipse and PM be the perpendicular on directrix .Then by definition of ellipse PF/PM = e PF 2 = e 2 PM 2 (x-p) 2 + (..

Composition of two functions or Product of two functions - Let f:AgB and g:AgB be two functions. Thus the composition of two functions f and g denoted by gof or fog is the function from A into C defined by gof = {(a,b) for some c B, (a,c) f and (c,b) g}.Let f..

The two expressions (LHS and RHS) are equal only for a particular value of the variable (x). These equations are called equations of condition. An equation of condition is generally referred to as an equatio..

Pair of straight lines is a family of lines through the point of intersection of two lines.There are different theorems to support the features and proofs for the existence of pair of straight line..

Summary - Finding the solution by the method of substitution. (i) Coefficients of one of the variables (say x) in the two equations are made equal, by multiplying them with suitable factor..