Question

(a) Transform the equation ^

2 − ^

2 − 2√2 − 10√2 + 2 = 0 after rotating

the axis through an angle 45°

.



(b) Determine the value of k so that the following equation will represent pair

of straight lines:

^

2 − + 2^

2 + 3 − 5 + 2 = 0​

Answer 1

Answer:

Figure 1. The nondegenerate conic sections

As we have seen, conic sections are formed when a plane intersects two right circular cones aligned tip to tip and extending infinitely far in opposite directions, which we also call a cone. The way in which we slice the cone will determine the type of conic section formed at the intersection. A circle is formed by slicing a cone with a plane perpendicular to the axis of symmetry of the cone. An ellipse is formed by slicing a single cone with a slanted plane not perpendicular to the axis of symmetry. A parabola is formed by slicing the plane through the top or bottom of the double-cone, whereas a hyperbola is formed when the plane slices both the top and bottom of the cone.

Answer 2

Answer:

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Step-by-step explanation:

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