**Intersection of two conic:**

**Intersection** between two conics **hyperbola and parabolas** are given.

**Hyperbola equation in the form**

**x² / a² – y² / b ² = 1 ……….. A**

and

**parabola form is**

**y ² = 4ax………………. B**

we fined the **point common** to both** Equation (A)** and** Equation (B)** we need to solve **equation A and equation B simultaneously.** We know **algebra** to solve the simultaneous solution set of two equation of the **second degree** consist of** four points.**

Thus, **two conics** will always interest in **four points.** These points may be all real and distinct,** two real** and t**wo imaginary**, or all imaginary.

**Two or more points may also coincide:**

Two conics are said to touch each other if they intersect in two or more confident point.

**Intersection of two conic example:**

**conic equation: 1**

**This equation can be written in the form:**

**3x² +4y² = 43 …………… A**

**Conic equation 2 of hyperbola**

we can write this equation in the form

**2x² – y² = 14 ………………. B**

Multiplying equation B by 4 and

adding the result into equation A. we get

**11x² = 99**

**x = ± 3**

**putting x= 3 in equation B**, we get result

18 – y ² = 14

y² = 4

**y = ± 2**

Thus,** (3, 2)and (3, -2)** are two point of intersection of the two conics.

And

**putting x = -3 into equation B** we get result

**y = ± 2**

**therefore, (-3, 2) and (-3, -2)** are also point of intersection

of equation A and B

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