Question

Identify the type of Conic and find centre, foci, vertices, and directrices of the following:

i) x² -2x + 8y +17 =0

____

⚠️ No galat Ancher..xD⚠️​

Answer 1

Answer:

∴x

2

+4y

2

+8y−2x+1=0

∴x

2

−2x+1+4y

2

+8y+2−1=0

(x−1)

2

+(2y+2)

2

−2=0

∴(x−1)

2

+(2y+2)

2

=2

∴

2

(x−1)

2

+(2)

2

2

(y+1)

2

=1

∴

2

(x−1)

2

+

1/2

(y+1)

2

=1

→x

1

=1 & y

1

=−1

Also,a=

2

&b=

2

1

centre =(1,−3)

→ majer axis=2a=2×

2

=2

2

→ minor axis=2b=2×

2

1

=

2

→e=

1−

a

2

b

2

e=

1−

2

1/2

=

1−

4

1

=

0

4

3

=

2

3

→ foci =(x

1

±ae,y

1

)=(1±

2

.

2

3

,−1)

=(1±

2

3

,−1)

→ length of latus =

a

2b

2

=

2

2×1/2

=

2

1

Step-by-step explanation:

if u won't understand answer

refer attachment janna❣️