Question

what is meant by X-intercept?

Answer 1

where value of y is zero in graph

Answer 2

The x-intercepts are the pionts where the graph crosses the x-axis.

To clarify the algebraic part, think again about the axes. When you were first introduced to the Cartesian plane, you were shown the regular number line from elementary school (the x-axis), and then shown how you could draw a perpendicular number line (the y-axis) through the zero point on the first number line. Take a closer look, and you'll see that the y-axis is also the line "x = 0". In the same way, the x-axis is also the line "y = 0".

Then, algebraically,

an x-intercept is a point on the graph where y is zero, and
x-intercept(s):y = 0 for the x-intercept(s), so:25x2 + 4y2 = 9 
25x2 + 4(0)2 = 9 
25x2 + 0 = 9 
x2 =  9/25 
x = ± ( 3/5 )Then the x-intercepts are the points ( 3/5, 0) and ( –3/5, 0)