free algebra 2 online

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..

The graph of a linear equation ax+by = c is a straight line. Two distinct lines always intersect at exactly one point unless they are parallel (have the same slope..

A hyperbola is the set of all points in the plane, the difference of whose distances from two fixed distinct points is a given positive constant that is less than the distance between the fixed point..

Summary - A function is a relation on A x B is which (i) no two second elements have a common first element. (ii) every first element has a corresponding second elemen..

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..

Let QPN be perpendicular to the major axis and O be the centre of the ellipse. Let NOQ=Φ,Then X = ON=OQcosΦ = acosΦ.Since p(x,y) lies on the ellipse (x 2 /a 2 )+(y 2 /b 2 ) = 1 and since x=acosΦ we have[( a 2 cos 2 &P..

Proof - Let QPN be perpendicular to the major axis and O be the centre of the ellipse. Let NOQ=Φ,Then X = ON=OQcosΦ = acosΦ.Since p(x,y) lies on the ellipse (x 2 /a 2 )+(y 2 /b 2 ) = 1 and since x=acosΦ we have[( a 2 cos 2 ..

x = 1, y = 1 is a solution of 2x + 3y = 5 2(1) + 3(1) = 5 x = -2, y = 3 is also a solution of 2x + 3y = 5 2(-2) + 3(3) = 5 -4 + 9 = 5 Similarly, we can find many more solutions for 2x + 3y ..

The condition for the line y=mx+c to touch the ellipse (x 2 /a 2 )+(y 2 /b 2 )=1 is that c =(a 2 m 2 +b 2..

1. i) Upto step 6 in the I Method and upto Step 7 in the II Method, gives the process of completing the square. ii) The quadratic equation has two roots. (i.e., there are two values for x) is b 2 - 4ac. This is usually denoted by D or D. D determines the nature..